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Full text of "Transactions of the Royal Society of Edinburgh"



.** 



-^— 




sjy 



TRANSACTIONS 



OF THE 



EOYAL SOCIETY OF EDINBUEGH 



tf.k.C.u. 



TRANSACTIONS 



OF THK 



ROYAL SOCIETY 



OF 



EDINBURGH. 



VOL. XXXIII. 




EDINBURGH: 

PUBLISHED BY ROBERT GRANT & SON, 107 PRINCES STREET, 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVEN T GARDEN, LONDON. 



MDCCCLXXXVIII. 



Part I. published . . • May 13, 1887. 

Part II. , ■ • • April 30, 1888. 

Part III. „ ... October 20, 1888. 



CONTENTS. 



PAET I. (1885-86.) 



PAGK 



I. The A tomic Weight of Tungsten. By John Waddell, B. A. , D. Sc. , 1 

II. On Dew. By John Aitken, F.R.S.E., .... 9 

III. On the Foundations of the Kinetic Theory of Gases. By Professor 

Tait, Sec. RS.R, . ... 65 

IV. The Eggs and Larva? of Teleosteans. By J. T. Cunningham, B.A., 

F.RS.E. (Plates I. -VII), ..... 97 

V. On the Fructification of some Ferns from the Carboniferous For 
mation. By Robert Kidston, F.R.S.E., F.G.S. (Plates VIII., 
IX.), . * .137 

VI. On the Colours of Thin Plates. By the Right Hon. Lord 

Rayleigh, Hon. F.R.S.E. (Plate X.), . . 157 

VII. On the Electrical Properties of Hydrogenised Palladium. By 
Cargill G. Knott, D.Sc. (Eclin.), F.R.S.E., Professor of 
Physics, Imperial University, Tokay o, Japan. (Plate XI.), . 171 

VIII. The Electrical Resistance of Nickel at High Temperatures. By 
Cargill G. Knott, D.Sc. (Edin.), F.R.S.E., Professor of 
Physics, Imperial University, Tokay o, Japan. (Plate XII.), . 187 

IX. The Formation of the Germinal Layers in Teleostei. By George 
Brook, F.R.S.E., F.L.S., Lecturer on Comparative Embryology 
in the University of Edinburgh. (Plates XIII. -XV.), . 199 



VI CONTENTS. 

PAG K 

X. On the Structure of Suberites domuncula, Olivi (0. S.), together 
with a Note on peculiar Capsules found on the Surface of 
Spongelia. By J. Arthur Thomson, F.R.S.E. (Plates XVI., 
XVIL), .241 

XI. The Reproductive Organs of Bdellostoma, and a Teleostean Ovum 
from West Coast of Africa. By J. T. Cunningham, B.A., 
F.R.S.K, ....... 247 



PART II. (1886-87.) 

XII. On the Foundations of the Kinetic Theory of Gases. II. By 

Professor Tait, Sec. R.S.E., . . . . .251 



XIII. Tables for facilitating the Computation of Differential Refraction 
in Position, A ngle, and Distance. By the Hon. Lord M'Laren 
F.R.S.E., . 

XIV. On a. Class of Alternating Functions. By Thomas Muir, LL.D 
F.R.S.E., 

XV. Expansion of Functions in terms of Linear, Cylindric, Spherical 
and Allied Functions. By P. Alexander, M.A. Communi 
cated by Dr T. Mum, F.R.S.E., 

XVI. On Cases of Instability in Open Structures. By E. Sang, LL.D. 
F.R.S.E., . 



279 



309 



31:3 



321 



XVIL On the Fossil Flora of the Radstock Series of the Somerset and 
Bristol Coal Field {Upper Coal Measures). Parts I., II. 
By Robert Kidston, F.R.S.E., F.G.S. (Plates XVIII. - 
XXVIIL), 335 

XVIII. A Diatomaceous Deposit from North Tolsta, Lewis. By John 
Rattray, M.A., B.Sc., F.R.S.E., of H.M. "Challenger" 
Commission, Edinburgh. (Plate XXIX.), . 419 

XIX. On the Minute Structure of the Eye in certain Cymothoida. By 
Frank E. Beddard, M.A., F.R.S.E., F.Z.S., Prosector to 
the Zoological Society, and Lecturer on Biology at Guy's 
Hospital. (Plate XXX.), . . . . .443 



CONTENTS. VII 

PAGR 

XX. Report on the Pennatulida dredged by H. M.S. "Porcupine." By 
A. Milnes Marshall, M.D., D.Sc, M.A., F.R.S., Beyer 
Professor of Zoology in the Owens College ; and G. H. 
Fowler, B.A., Ph.D., Berkeley Fellow of the Owens College, 
Manchester. Communicated by John Murray, Esq. (Plates 
XXXI., XXXIL), ...... 453 

XXI. On the Determination of the Curve, on one of the Coordinate Planes, 
which forms the Outer Limit of the Positions of the Point of 
Contact of an Ellipsoid which always touches the three Planes of 
Reference. By G. Plarr, Docteur es-sciences. Communi- 
cated by Professor Tait, ..... 465 

XXII. On the Partition of Energy between the Translatory and Rotational 
Motions of a Set of Non-Homogeneous Elastic Spheres. By 
Professor W. Burnslde, . . . . .501 

XXIII. A Contribution to our Knowledge of the Physical Properties of 

Methyl-Alcohol. By W. Dittmar, F.RSS. Lond. & Edin., 

and Charles A. Fawsitt. (Plate XXXIII. ), . . 509 

XXIV. On the Thermal Conductivity of Iron, Copper, and German Silver. 

By A. Crichton Mitchell, Esq. Communicated, with an 
Introduction, by Professor Tait, Sec. R.S.E. (Plates 
XXXIV., XXXV.), 535 

XXV. Critical Experiments on the Chloroplatinate Method for the De- 
termination of Potassium, Rubidium, and Ammonium ; and a 
Redetermination of the A tomic Weight of Platinum. By W. 
Dittmar, F.R.S.E., and John M'Arthur, F.RS.E., . 561 



PART III. (1887-88.) 

XXVI. The Polychaeta Sedentaria of the Firth of Forth. By J. T. 
Cunningham, B.A., Fellow of University College, Oxford, 
F.RS.E., Superintendent of the Granton Marine Laboratory; 
and G. A. Ramage, Vans Dunlop Scholar in Edinburgh Uni- 
versity. (Plates XXXVI. -XL VII.), . . . 635 



PAGE 



viii CONTENTS. 

Appendix — 

The Council of the Society, . 688 

Alphabetical List of the Ordinary Fellows, . . . 689 

List of Honorary Fellows, ..... 702 

List of Or dinary Fellows Elected during Session 1886-87, . 704 

Laws of the Society, . . . . . .709 

The Keith, Makdougall-Brisbane, Neill, and Victoria Jubilee 

Prizes, . . . . . .714 

Awards of the Keith, Makdougall-Brisbane, Neill, and Victoria 

Jubilee Prizes, . . . . . .717 

Proceedings of Statutory General Meeting, . . .721 

List of Public Institutions and Individuals entitled to receive Copies 

of the Transactions and Proceedings, . . .725 

Index, ........ 731 



25 FEB18B9 



26 JUL 1887 



TRANSACTIONS 



OK THE 



EOYAL SOCIETY OF EDINBURGH. 

VOL. XXXIII. PART I.— FOR THE SESSION 1885-86. 



CONTENTS. 



Page 
Art. I. The Atomic Weight of Tungsten. By John Waddell, B.A., D.Sc, . . 1 

II. On Dew. By Mr John Aitken, ...... 9 

III. On the Foundations of the Kinetic Theory of Gases. By Professor Tait, . . 65 

IV. The Eggs and Larvae of Teleosteans. By J. T. Cunningham, B.A. (Plates I. to 

VII.), 97 

V. On the Fructification of some Ferns from the Carboniferous Formation. By 

Robert Kidston, F.R.S.E., F.G.S. (Plates VIII., IX.), . . .137 

VI. On the Colours of Thin Plates. By Lord Rayleigh. (Plate X.), . . 157 

VII. On the Electrical Properties of Hydrogenised Palladium. By Cahgill G. Knott, 
D.Sc. (Edin.), F.R.S.E., Professor of Physics, Imperial University, Tokayo, 
Japan. (Plate XL), ........ 171 

VIII. The Electrical Resistance of Nickel at High Temperatures. By Cargill G. Knott, 
D.Sc. (Edin.), E.R.S.E., Professor of Physics, Imperial University, Tokayo, 
Japan. (Plate XII.), . . . . .187 

IX. The Formation of the Germinal Layers in Teleostei. By George Brook, F.L.S. 
Lecturer on Comparative Embryology in the University of Edinburgh. 
(Plates XIII. to XV.), . . . . . . .199 

X. On the Structure of Suberites dotnuncula, Olivi (0 .#.), together with a Note on 
pecidiar Capsules found on the Surface of Spongelia. By J. Arthur Thomson. 
(Plates XVI., XVII.), 241 

XL The Reproductive Organs of Bdellostoma and Teleostean Ovum, from West Coast of , 

Africa. By J. T. Cunningham, B.A., ..... 247 



[Issued May SI, 1887 A 



\ 



T B A N S A C T I N S. 



I. — The Atomic Weight of Tungsten. By John Waddell, B.A., D.Sc. 

(Read 7th June 1886.) 

From the results obtained by Berzelius in his experiments with tungsten, 
the number 189 "28 is calculated as the atomic weight of that metal. Many 
later investigations have been made, in which uniformly a lower figure was 
arrived at, in the majority of cases very nearly 184, which has therefore been 
regarded as the atomic weight. 

Some of the determinations were made with a special view to the support 
or overthrow of a theory. Dumas, for instance, wished to discover whether the 
atomic weight of tungsten was exactly double that of molybdenum. In such 
cases it would be natural to suppose that special care would be taken to 
secure purity of materials. Dumas obtained the numbers 96 and 184 as the 
atomic weights of molybdenum and tungsten, but he seems to have distrusted 
his results ; for he remarks — " Is it necessary, however, to conclude from this 
discussion, that some simple ratios of the kind which one used to admit between 
molybdenum and tungsten cannot exist? I do not think so " {Ann. Chim. Phys., 
[3] 55, 144). 

In studying the literature of the subject, I felt that no security was afforded 
by the various experimenters of the purity of the compounds made use of by 
them. Scheibler (Jour. Prac. Chem., 83, 273), apparently considers a single 
recrystallisation of the sodium salt all that is necessary. This salt was used as 
a starting point, and though the further working up into barium metatungstate 
may have tended to purification, Scheibler certainly does not prove that he 
has thus freed his tungsten from molybdenum and silicon. Bernoulli (Pogg. 
Ann., Ill, 573) considered that he had obtained pure tungstic acid, though he 
gives no indication of an attempt to free from molybdenum. He prepared his 
tungstic acid from wolfram, which contained silica and niobic acid, from which 

VOL. XXXIII. PART I. A 



2 DR JOHN WADDELL ON 

the tungstic acid was separated by solution in ammonia. He found that the 
reduced metal, when ignited in a current of chlorine, was entirely changed into 
a volatile chloride. This test proves the absence of silica, which would have 
formed a residue, but has no bearing whatever upon the question, whether or 
no molybdenum were present; for molybdenum pentachloride, and tungsten 
hexachloridc are produced under precisely the same conditions, and are very 
similar in appearance and characteristics. 

Similar criticisms could be made on all the investigations to which I have 
referred. It appeared to be too readily assumed that recrystallisation would 
insure purity, no certainty being afforded either by a trustworthy mode of 
separation of all possible impurities, or by tests showing the absence of 
admixture. 

In my work. I kept specially in view the elimination of silicon and molyb- 
denum, at the same time using all precautions to free from other impurities as 
well. 

The reason for paying special attention to silicon and molybdenum, was 
that these are very similar in many respects to tungsten, and are moreover very 
liable to exist in ores of that metal. The presence of both was proved in some 
scheelite with which preliminary experiments were made, and their elimination 
was found to be no very easy matter. 

The material used as starting point in the subsequent investigation was 
commercial tungsten, a dark grey powder, containing 94-98 per cent, of the metal. 
The impurity was supposed by the manufacturers to be chiefly lower oxides of 
tungsten, and in particular molybdenum was said to be absent. The employ- 
ment of metallic tungsten as starting point is not to be recommended, owing to 
the great difficulty of oxidation. The most convenient material, doubtless, is 
sodium tungstate, which can be obtained readily enough. In my work, how- 
ever, some interesting facts with regard to oxidation were brought into 
prominence, for I tried several methods, the results of which are here given. 

The first mode of oxidation tested was continued boiling with aqua regia, 
but at the end of a week a great deal of the metal was still unacted upon, and 
the method was considered unsatisfactory. 

Another plan tried was mixing the metal with nitre, and throwing the 
mixture, small portions at a time, into a red hot crucible. Moderately good 
results were thus obtained; and the process would, I think, work fairly well 
on the large scale where proper furnaces and crucibles are available. On 
the small scale, the chief objection is that the crucible itself is attacked. A 
third method furnished good results, and considerable attention was devoted to 
the determination of the most favourable conditions. The process consisted in 
the ignition of a mixture of potassium chlorate, sugar, and metal. After an ex- 
tended number of trials, the proportions found most satisfactory were 9 : 3 : 5. 



THE A.TOMIC WEIGHT OF TUNGSTEN. 3 

This is the most expeditious method of oxidation, for 200 grammes of metal 
can readily be ignited in one operation, and two-thirds of the total quantity are 
oxidised in a few seconds. I found it most convenient to mould the materials 
into a cone, sufficient water having been added to make this operation possible. 
The cone having been placed on a large iron tray was lighted at the apex, so 
that the propagation of the combustion was downward. By this precaution, 
loss of material caused by spurting was in large measure avoided. The 
objection to this mode of oxidationis the great difficulty experienced in re- 
covering tungstic acid from the great bulk of salt. If, however, appliances are 
at hand for evaporation, with strong hydrochloric acid on an oil bath and long 
continued drying at 120°, the process might be made fairly successful, otherwise 
the difficulties encountered in recovering the tungstic acid far outweigh the 
advantage gained by rapid oxidation. 

The method which I found most convenient and satisfactory was the igni- 
tion of the metal in a porcelain tube, a current of air being passed over the 
red hot mass. The metal must form only a thin layer, else the oxidised 
material will obstruct the passage of air, for tungstic acid occupies nearly 
four times the volume of metallic tungsten. In my experiments, sulphurous 
fumes were produced in considerable quantity, evidently showing the presence 
of sulphide in the commercial tungsten. The vapours were absorbed by 
caustic soda solution, and in this solution traces of molybdenum were found. 
After about six hours' heating, the metal was, as a rule, to a great extent 
oxidised, and had acquired a green colour. If the operation be long continued, 
say for thirty hours, the compound produced possesses a canary-yellow colour, 
and is practically tungstic acid. 

The green colour usually obtained was doubtless due to the presence of 
partially oxidised and totally unoxidised material. In ordinary cases complete 
oxidisation was not considered necessary, for in subsequent operations the 
small amount which had escaped the action of the hot air was easily elimin- 
ated. The greater part of the tungstate obtained was prepared from the im- 
pure tungstic acid just mentioned. The mode of treatment was as follows : — 

The partially oxidised mass was fused in a platinum basin with one half of 
its weight of sodium carbonate. The fusion was complete in a few minutes. 
The fused mass after cooling was disintegrated with water, and the tungstate 
dissolved out, leaving the unoxidised metal as residue. It was found that the 
platinum basin was somewhat attacked, and subsequent examination proved 
the presence of lead in the tungsten residue. The solution of tungstate was 
boiled in a large silver basin with addition of ammonia carbonate, the latter 
being employed to separate out any silica or iron and aluminium hydrates 
possibly present. A very slight precipitate formed and was filtered off. The 
filtrate was again treated with ammonium carbonate, the process being repeated 



4 DR JOHN WADDELL ON 

till no more precipitate was produced. The liquid was then evaporated to 
dryness, and thus a mixture of sodium tungstate and carbonate was obtained. 
For my purpose the presence of carbonate was no disadvantage, and I did not 
crystallise out the tungstate. 

As I have already remarked, the method of purification hitherto almost 
universally adopted was recrystallisation. I employed the method of fractional 
precipitation as more likely to give a decided test. In the case of all the 
precipitations being alike, the probability of purity would nearly amount to a 
certainty, for it is extremely unlikely that the proportions of the impurities 
would be the same in each of the precipitates. In case of a difference 
appearing in the precipitations, it is natural to suppose that those most widely 
separated would exhibit the greatest dissimilarity, and that the middle frac- 
tionations would be similar and practically pure. 

It was known that the great bulk of my salt was tungstate. Any impurities 
more readily precipitated than tungsten ought to be concentrated in the first 
fractionation, while anything less readily precipitated would be chiefly found 
in the last portion. 

The question presented itself in what form it was best to precipitate the 
tungsten. From the soluble tungstate it was possible to throw down either an 
insoluble tungstate or tungstic acid. As I wished to determine the atomic 
weight of the metal by reduction of tungstic acid, it is evident that if the 
former method were employed it would be well to produce a tungstate which 
could be easily decomposed and changed to tungstic acid. Such a compound 
is mercurous tungstate, which loses its mercury on ignition. From some 
experiments tried with mercurous nitrate as precipitant, I decided that this 
method of fractionation was not so feasible as the precipitation of tungstic 
acid direct by means of hydrochloric acid. 

Before proceeding with the fractionation, however, I freed the sodium 
tungstate so far as possible from molybdenum. The method employed was 
that recommended by Rose. Sufficient tartaric acid was added to a solution 
of the alkaline salt to prevent the precipitation of tungstic acid on acidification 
with hydrochloric acid. A stream of hydrogen sulphide was then passed 
through the solution, and an appreciable though small precipitate of molyb- 
denum sulphide was thus obtained. 

The filtered solution containing about 300 grammes of solid tungstate had 
a blue colour, owing to the presence of a small quantity of one of the lower 
oxides of tungsten. The liquid was decolorised by the passage of a current 
of air, and was then ready for fractional precipitation. It is to be noted that 
though sufficient tartaric acid had been added to the solution to prevent 
precipitation of tungstic acid by a small quantity of dilute hydrochloric acid, 
yet a considerable excess of the latter was capable of producing quite a pre- 



THE ATOMIC WEIGHT OF TUNGSTEN. 5 

cipitate. This fact is important, otherwise the method must have been greatly 
modified. It is further to be noted that the precipitation was gradual, hence 
there was ample opportunity for the liquid to be well mixed, and the precipi- 
tation was therefore not of a local character. The mode of procedure was the 
following : — 

The liquid was boiled in a porcelain basin, and to it a measured quantity of 
pure hydrochloric acid was added. The boiling was then continued till the 
precipitate was formed in sufficient quantity, when the contents of the basin 
were removed to a large beaker and allowed to settle. The supernatant liquid 
was after some time decanted, and the precipitate washed once or twice by 
decantation. The precipitate was set aside for future use, the separate 
decantations were united and evaporated to the bulk of the original solution, 
and acid added as before. This process was repeated till eleven fractionations 
were obtained. 

The first of these had a dark green colour, probably because the current of 
air had not thoroughly oxidised the liquid. The subsequent precipitates, as 
far as the seventh, were pale yellow ; while the remaining fractionations were 
dirty green, and not so finely divided as those which preceded. These 
differences were, I think, caused by the fact that for the final precipitations the 
liquid required to be boiled clown to small bulk, in order to obtain a reasonable 
quantity of tungstic acid. The tartaric acid under these circumstances 
probably exercises a reducing action, and in the small quantity of liquid the 
precipitate was in all likelihood aggregated by the continued boiling. 

The third precipitate was purified, and used for estimation of the atomic 
weight. The precipitate was washed several times by decantation, and then 
repeatedly on a filter. It was then dissolved in pure ammonia, and after 
filtration reprecipitated by addition of pure hydrochloric acid. The solution in 
ammonia had a triple purpose. It insured the oxidation of the precipitate 
in case any lower oxide of tungsten were present. It separated any slight 
trace of impurity not soluble in ammonia. It aided the washing from sodium 
salts, for the solution and reprecipitation presented fresh surfaces to the action 
of the wash water. The washing (which was with water containing a little 
hydrochloric acid in order to prevent the precipitate running through the filter) 
was continued till the filtrate yielded no residue on evaporation, and a test 
portion of the precipitate gave only a slight indication of sodium by the spectro- 
scope. The precipitate was afterwards dried and ignited in a current of air. The 
tungstic acid thus obtained had a beautiful pale canary- yellow colour, and was 
quite uniform in appearance. It was reduced in a porcelain tube by a current 
of pure hydrogen, the temperature being gradually raised from below dull 
redness to the highest obtainable by a strong blast in a Fletcher's furnace. 

Assuming that tungstic acid has the composition expressed by the formula 



(5 



DR JOHN WADDELL ON 



W0 3 , and that it is reduced to metallic tungsten by ignition in a stream of 
hydrogen, the weight of oxygen lost, compared with that of the tungsten left 
behind, gives all the data required for determining the atomic weight of the 
latter. As a mean of three experiments made with the precipitate described, 
I obtained the number 184-5. The tenth and eleventh precipitates were united, 
and treated in the same way as the third fractionation. It was difficult to 
wash, and the tungstic acid had a greenish tinge, and altogether did not appear 
so pure as what had been before obtained. During the reduction there was a 
slight volatilisation. The atomic weight, estimated in this sample, was 183*7. 
The seventh precipitate was subjected to similar treatment. Its appearance 
and behaviour were quite satisfactory, and the atomic weight calculated was 
184. I made a number of other determinations which need not be described. 
Some of them were made with tungstic acid not freed from molybdenum by 
sulphuretted hydrogen. In a number of cases a slight volatilisation was 
observed, and in these the atomic weight estimated was low. So uniformly 
was the volatilisation noticed when the number obtained was below 184, that 
there is every reason to believe that where no volatilisation was observed none 
actually occurred. 

The uniformity in result was greatly in favour of purity in the tungstic acid; 
but as silica is with difficulty precipitated from a silicate by means of hydro- 
chloric acid, and as tungstic acid exhibits the same characteristics, I thought 
it advisable, if possible, to prove the absence of silica independently. This I 
did by Marignac's method of separation, which consists in fusing with hydrogen 
potassium sulphate. Tungstic acid forms a tungstate under these circum- 
stances, while silica remains unaltered, and is left undissolved when the fused 
mass is treated with water. As no residue was left after solution, the absence 
of silica was established. 

Subjoined is a table of the estimations described above : — 



Fraction. 


wo 3 . 


W left. 


3 lost. 


Atom weight. 


Remarks. 


III. 

VII 

X. 


1-4006 
•9900 

1-1479 
•9894 

4-5639 


11115 

•7855 

•9110 

•7847 

3-6201 


•2891 
•2045 
•2369 
•2047 
•9438 


184-55 
184-37 
184-59 
184-00 
183-69 


No volatilisation. 

» 

»> 

Slight volatilisation. 



Of the above determinations, those denoted III. are the most trustworthy, from 
the fact that there are three concordant estimations. The mean of these is 
184 - 5, which is the atomic weight of tungsten calculated from oxygen equal 16. 

This reduced to = 15*90 gives W = 18404. 

I made a couple of determinations of the specific gravity of two specimens 



THE ATOMIC WEIGHT OF TUNGSTEN. 7 

of metallic tungsten, the first A had not been specially freed from molybdenum, 
the second B was a portion of III. The determinations were made in a 
specific gravity bottle of 10 c.c. capacity. The bottle was weighed empty, and 
full of distilled water which had been boiled to expel air. The bottle was 
then dried and weighed again, then some tungsten was introduced, and another 
weighing was made. The metal was afterwards covered with water, and the 
bottle placed under an air-pump, in order to extract the air enclosed in the 
powder. The bottle was then filled with water, and a weighing again made, 
and as the water evaporated slowly, but perceptibly, weighings were taken 
when the meniscus in the capillary touched two fixed marks scratched on the 
stopper. How nearly the readings agreed, is shown in the table below. 



Specimen. 


Wt. tungsten. 


Reading. 


Weight water 
displaced. 


Specific gravity. 


A 
B 


1-0353 
■7187 


Upper mark 
Lower mark 
Upper mark 
Lower mark 


•0566 
■0566 
•0382 
•0383 


18-249 
18-249 
18-772 
18-765 



Most reliance should be placed upon the result obtained with B, because of 
the assured purity of the metal, and because a first trial would be liable to 
experimental errors. All such errors tend to give a low specific gravity. 

It was not thought necessary to make another determination, because the 
number agrees so well with those obtained by the best authorities. The 
highest determination is that given by Roscoe, viz., 1913; the majority of 
experimenters give figures lying between 18 and 19, while a number so low as 
16-54 has been obtained. The density seems to depend upon the method of 
preparing the metal. 

My work has been confirmatory of the commonly accepted atomic weight 
and specific gravity of tungsten ; its chief value lies in the fact that the subject 
was attacked in a way so far as I know not hitherto attempted, and the corro- 
borative evidence is therefore all the more trustworthy. 

My thanks are due to Prof. Crum Brown and Dr Gibson for valuable 
suggestions and kindly assistance. 



( » ) 



II. — On Dew. By Mr John Aitken. 

(Read 21st December 1885.) 

The immense amount that has been written on the subject of dew renders it 
extremely difficult for one to state anything regarding it which has not been 
previously expressed in some form. It has been examined over and over by 
minds of every type, and from every point of view; so that every possible 
explanation of the different phenomena seems to have been given, and so many 
passing thoughts recorded, that from the literary point of view the whole 
subject seems exhausted. As a necessary result, these different treatises 
are in many respects contradictory; and it would be quite impossible to 
construct anything like a consistent explanation and account of our subject^ 
from the very voluminous writings of those who have treated it from the purely 
literary point of view, and whose ideas have been evolved from their inner 
consciousness, according to what seemed to them the fitness of things, and 
without questioning nature as to the truth of their conclusions. On the 
scientific side of the subject, however, the writings are not so voluminous, and 
additions to it are still required to enable us to determine which of the many 
conflicting opinions are correct. 

In ancient times it was thought that the moon and stars had an important 
influence on dew, probably because there is most dew on those nights when 
these orbs shine brightly on the earth; thus confusing two things which have a 
common cause, and making one the effect of the other. Aristotle placed the 
knowledge of this subject far in advance of his time. He defines dew to be 
humidity detached in minute particles from the clear chill atmosphere. The 
Romans, led by the writings of Pliny, returned again to the primitive idea that 
dew fell from the heavens. This idea retained its position during the course of 
the Middle Ages. Then began an endless variety of theories, such as, that the air 
is condensed into water by the cold, that the moon's rays caused it, and so on. 

In the beginning of the eighteenth century clearer ideas began to be formed, 
and a reformation took place, in which, as in most reformations, the swing of 
the pendulum went to the extreme on the opposite side. Dew was no longer 
believed to descend from the heavens, for Gersten advanced the idea that it 
rose from the earth ; and in this opinion he was followed by M. Du Fay and 
Professor Musschenbroek, the latter, however, afterwards made some observa- 
tions which caused him to change his opinion. Gersten was led to think that 
dew rose from the ground, because he often found grass and low shrubs moist 

VOL. XXXIII. part i. B 



10 MR JOHN AITKEN ON DEW. 

with it, while trees were dry. M. Du Fay followed up these observations with 
experiments, made by placing sheets of glass at different heights from the ground. 
He found that dew formed on the lowest pane first, and only appeared on the 
highest at a later hour; he also found that the lowest pane collected most 
moisture. Other observers gave somewhat different explanations of the pheno- 
mena connected with dew; but owing to a want of clearness, the subject did not 
advance much till the masterly Essay on Deiv by Dr Wells made its appearance. 

Dr Wells' experiments were so simple, and his interpretation of the different 
phenomena connected with dew so clear, that he has been justly considered the 
great master of this subject. In his Essay he struck a medium between the 
two previous theories as to the source of the moisture that forms dew. He 
did not think with the ancients that it fell from heaven, nor with Gersten that 
it rose from the earth, but that it was simply condensed out of the air in 
contact with the surfaces of bodies cooled by radiation below the dew-point of 
the air at the place. This opinion has, so far as I am aware, been generally 
received up to the present time. 

Some experiments I have recently made on this subject have caused me to 
differ entirely from Dr Wells as to the source of the vapour that forms clew. 
As everything written by Dr Wells is, so to speak, stereotyped and final, there 
seems to be the greater reason that any of his conclusions that seem doubtful 
should be carefully criticised and fully investigated; I shall therefore give an 
account of the experiments that have caused me to differ from so great an 
authority. 

Dr Wells thought that almost all the moisture deposited as dew at night 
was taken up by the air during the heat of the day ; so that, according to his 
idea, vapour ascended from the earth during the day, and again descended and 
became condensed as dew on the surface of the earth at night. My observa- 
tions have led me to the very opposite conclusion. All my experiments indicate 
that dew, on bodies near the surface of the earth, is almost entirely formed 
from the vapour rising at the time from the ground; at least this would appear to 
be the case generally in this climate, to which my experiments have been confined. 

After Gersten gave his reasons for supposing that dew rose from the 
ground, and Du Fay extended the subject, Dr Wells combated their conclu- 
sions, and successfully showed that their experiments did not prove that 
vapour rose from the ground, and that all the phenomena adduced in favour of 
their theory could be equally well explained according to his own. With 
regard to Du Fay's reason for thinking that dew rises from the ground — 
namely, that it appears on bodies near the earth earlier than on those at a 
greater height — he says :* " But this fact readily admits of an explanation on 
other grounds, that have already been mentioned. 1. The lower air, on a 

*An Essay on Dew, by William Charles Wells, p. 109. 



MR JOHN AITKEN ON DEW. 11 

clear and calm evening, is colder than the upper, and will, therefore, be sooner 
in a condition to deposit a part of its moisture. 2. It is less liable to agitation 
than the upper. 3. It contains more moisture than the upper, from receiving 
the last which has risen from the earth, in addition to what it had previously 
possessed in common with other parts of the atmosphere." Then he goes on to 
give reasons why vapour cannot be rising out of the ground, but adds, that some 
of it must be from this source, as bodies near the surface of the ground get dewed 
sooner than those higher up, though equally cold with them, but says, " the 
quantity from this cause can never be great," and proceeds to give his reasons, 
which are not altogether satisfactory, and need not be quoted here. He then 

sums up as follows : — " These considerations warrant me to conclude 

that on nights favourable to the production of dew, only a very small part of 
what occurs is owing to vapour rising from the earth ; though I am acquainted 
with no means of determining the proportion of this part to the whole." 

I shall now proceed to detail the observations which have caused me to 
differ from the conclusion so distinctly set forth by Dr Wells in the above 
quotations. I need not say that all my experiments only confirm the con- 
clusions of that observer as to the formation of dew — that is, as to the 
conditions most favourable for the deposition of moisture on the surfaces of 
bodies during dewy nights, while the earth is radiating heat into space. The 
point on which we differ is as to the source of the vapour that condenses 
on the radiating surfaces — -a point which Dr Wells admits there were no 
facts to determine, his own opinion being formed by experiments that did not 
bear directly on the subject. 

When I began to doubt the truth of the generally received opinion as to the 
source of the vapour, I found a difficulty in beginning my investigation, as it 
was not easy to arrange experiments to give a direct answer to the question. 
My intention at first was to test, by means of a delicate hygrometer, the 
humidity of the air at different heights from the ground and under different 
conditions. This plan had, however, soon to be abandoned, owing to the 
impossibility of making anything like accurate observations with any 
instruments at present in use. 

For some time I have had in my possession a hair hygrometer constructed 
by Chevallier of Paris, This form of instrument is perhaps one of the best 
for the purpose ; yet on making a few test experiments with it, for the special 
purpose under consideration, its indications were found to be nearly valueless. 
For instance, if the instrument was removed from saturated to drier air, and 
again replaced in the saturated, it was impossible to get the pointer back 
again to the same position on the scale ; and as the amount of dryness it would 
be required to measure was a very small degree removed from saturation, the 
error in the indications might be greater than the actual amount of dryness. 



12 MR JOHN AITKEN ON DEW. 

Then again, all such hygrometers, as well as wet and dry bulb thermometers, 
will have their indications affected by radiation ; they will surround themselves 
with an envelope of cooled air, as there is but little wind during the time the 
observations require to be made. Their indications would therefore be of little 
value, and investigation by means of them had to be abandoned. 

What first caused me to doubt the present theory, and led me to suppose 
that dew is formed from vapour rising from the ground, was the result of some 
observations made in summer on the temperature of the soil at a small depth 
under the surface, and of the air over it, after sunset and at night. On all 
occasions in which these temperatures were taken, the ground a little below 
the surface was found to be warmer than the air over it. It is evident that, so 
long as these conditions exist, and provided the supply of heat is sufficient to 
keep the surface of the ground above the dew-point, there will be a tendency 
for vapour to rise and pass from the ground into the air, the moist air so 
formed will mingle with the air above it, and its moisture will be condensed, 
forming dew wherever it comes in contact with a surface cooled below its 
dew-point. 

These considerations suggested another method of experimenting than by 
the use of hygrometers. If vapour is really rising from the ground during 
night, it seemed possible that it might be trapped on its passage to the air, 
and that this might be accomplished by placing over the soil something 
that would check the passage of the vapour, while it allowed the heat to 
escape. To carry out this idea, I placed over the soil shallow boxes or trays, 
made of tinplate and painted. These trays were 3 inches (76 mm.) deep, 
and more than a foot (305 mm.) square in area; they were placed in an 
inverted position over the soil to be tested. 

The action of these trays will be somewhat as follows : — Supposing the 
roof of the small enclosure formed by the covering tray is not by the passing 
air or by radiation cooled below the temperature of the ground. Then 
evaporation will cease when the air between the tray and the ground is 
saturated, and no dew will collect on the inside of the enclosure. But if the 
tray is cooled below the temperature of the ground, vapour will condense on the 
inside, and more vapour will rise from the ground to supply its place, and this 
will go on so long as the ground is the warmer of the two. The effect of these 
trays will be very much the same as if there was no enclosure, and the air 
over the grass was nearly saturated, motionless, and of a lower temperature 
than the soil. But it is evident the trays will check the evaporation on most 
nights, on account of the slow circulation inside, and also on account of the 
air inside being always nearly saturated, which is not the case outside the 
enclosure, so that under most conditions.it seems likely there will be less 
evaporation under the trays than outside them. This will be particularly the 



MR JOHN AITKEN ON DEW. 13 

case on those nights when there is wind, and the air is not saturated, a con- 
dition which seems to be very frequent in our climate at ordinary elevations. 
We must remember that the air may not be saturated when dew is forming; and 
the dew-collecting surface requires to be cooled below the temperature of the 
air before it collects moisture. 

In experimenting with these trays different kinds of ground were selected, 
and the trays placed over them after sunset, that is, after the earth had ceased 
to receive heat, and the heat-tide had begun to ebb. They were generally 
examined between 10 and 11 p.m., and again in the morning. 

Dew on Grass. 

Confining our attention to the trays placed over grass, the result of the 
experiments was that, on all occasions yet observed, there was — 1. Always 
more moisture on the grass inside the trays than outside. 2. There was always 
a deposit of dew inside the trays. 3. There was often a deposit outside the 
trays, but the deposit on the outside was always less than on the inside, and 
sometimes there was no deposit outside when there was one inside. 

Now I think these facts prove that far more vapour rises out of the ground 
during the night than condenses as dew on the grass. This excess is evidenced 
by the greater amount of moisture on the grass inside the trays than outside, 
and by the amount of dew condensed inside the box. Under the ordinary con- 
ditions found in nature, this excess is carried away by the wind and mixed up 
with the air, while some of it is deposited on bodies further away from the ground. 
It should be noticed that the inside of the tray was more heavily dewed than 
the outside. This shows there was a higher vapour tension inside than outside 
the enclosure, which proved that the vapour rising from the ground outside 
the tray had got mixed up with drier air, as it did not form so heavy a coating 
of dew as the inside air, even though it had the advantage of a slightly lower 
temperature than the inside, on account of it being the side of the metal 
from which the heat was radiating. 

It may be as well to notice here some objections that may be made to this 
way of testing the point. It may be said, that though so much vapour does 
rise under these trays, yet if they were removed and the grass freely exposed, 
the vapour would not rise, and that the vapour rises because the tray keeps 
the ground under it warm. Observation certainly shows that the ground under 
the trays is kept slightly warmer than outside them. At night a ther- 
mometer is higher on the grass under the tray than on that outside, and next 
morning the ground at 3 inches below the surface is from 1 to 2 degrees warmer 
under the tray than outside its influence. This objection to the protecting 
influence of the trays has an appearance of reason about it; but if we examine 
the facts, I think it will be admitted that instead of being an argument 



14 MR JOHN AITKEN ON DEW. 

against this method of experimenting it is rather a reason for it. We must 
remember the tray does not heat the ground ; it does not add anything to its 
store of heat, and enable it to evaporate more moisture ; it simply prevents so 
much of its store of heat escaping. Now heat escapes from the ground at 
night in two ways — first, by radiation, and second, by absorption — to supply the 
latent heat of evaporation. From the area covered by these trays radiation 
goes on much as at other places ; the painted metal will radiate as much heat 
as the grass, but evaporation is checked, as there is but little circulation under 
the trays ; and further, there is the heat recovered by the condensation 
inside the box. It would thus appear that the reduced evaporation and heat 
of condensation will be the principal causes of the higher temperature inside 
than outside ; so that the trays, instead of increasing the evaporation, would 
rather seem to decrease it; and that the lower temperature outside is due to 
the greater evaporation there taking place, as both surfaces are exposed to the 
same loss by radiation. 

There is an objection that might be made to the whole theory that dew is 
formed from vapour rising from the ground. It might be urged that it is 
impossible for the vapour to rise from the ground, and that these trays interfere 
with the conditions existing in nature. On a cold clear night, for instance, when 
the grass gets cooled before the dew-point, it might be said that it is quite 
impossible for the vapour to rise up through it, as it would be all trapped on 
its passage to the surface by contact with the cold blades, and that the trays 
placed over the grass prevent this condensation by stopping the radiation from 
the grass, and thus they allow the vapour to come up. 

A little explanation will, however, show this objection to be groundless. 
On a dewy night no doubt the top of the grass is at a temperature below the 
clew point, and if Ave may take the temperature of a thermometer placed on the 
grass to be the same as that of the grass, which we may do without sensible 
error, if we then remove the thermometer and place it among the stems of the 
grass, the thermometer will rise; and if we place the bulb among the stems close 
to, but not in the ground, we shall find it to be very much warmer than at the 
surface. On dewy nights I have frequently found it as much as 10 to 12 
degrees warmer. From this we see that the warm air diffusing upwards with 
its burden of vapour only meets with a very small amount of surface cooled 
below the dew-point, so that the greater part of the vapour is free to escape 
into the air. 

Fairly considered, I think these trays more nearly represent natural 
conditions than might at first sight appear. Indeed, precisely similar results 
have been observed with natural conditions. If we examine plants with large 
blades, we shall often find, on dewy nights, that those leaves which are close to 
the ground have their under surfaces heavily dewed, while their upper surfaces 



MR JOHN AITKEN ON DEW. 15 

are dry. The effect of the trays is very much the same as that of these large 
leaves on a perfectly calm night. The only difference is, the trays will lose 
more heat on account of their better conducting power, and more vapour will 
be condensed under them than under the bad conductor, while the temperature 
of the soil will be more nearly reduced to what it would have been if no large 
close surface prevented the free evaporation. 

The experiments described were made in August and September, when the 
ground was very dry, owing to the unusually small rainfall during the previous 
months. On all occasions the inside of the tray was dewed, however dry the 
soil, and the inside was always more moist than the outside. 

After these experiments were made, another method of testing the point 
under investigation suggested itself, and though, unfortunately, rather far on 
in the season for satisfactory work of this kind, I at once proceeded to carry it 
out, as it afforded a means of checking my previous experiments with the 
trays ; but by this time October had arrived, and the conditions had very much 
changed. The temperature had fallen considerably, and the rainfall had greatly 
increased the humidity of the soil. 

It is very evident that if vapour continues to rise from the ground during 
dewy nights, as well as during the day, the ground giving off vapour must 
lose weight. If this could be shown to be the case, it would prove in a more 
satisfactory manner than the previous experiments that vapour does rise from 
the ground during night, and that, therefore, dew on bodies near the surface 
of the ground is really formed from the vapour rising at the time, and not from 
the vapour that rose during the day. 

In the first week of October experiments were begun to test this point, by 
weighing a small area of the surface of the ground, before and after dew had 
formed, to see whether the ground continued to give off vapour or not while 
dew was forming. For this purpose a number of shallow pans 6 inches 
(152 mm.) square and \ inch (6 - 3 mm.) deep were prepared. One of these 
pans was selected, and a piece of turf slightly smaller was cut from the lawn 
and placed in it. The pan with its turf was then carefully weighed with a 
balance sensitive enough to turn with ^ grain; but in experiments of this kind, 
which must be done quickly, accuracy of only one grain was aimed at, lest the 
time required for more accurate weighing might cause loss of weight by evapora- 
tion. To prevent loss from this cause, the weighing was clone in an open shed. 

The turf was cut at sundown, and when dew began to form. The earth 
was removed from it till it weighed exactly 3500 grains (226*79 grammes). 
The pan with its turf was then rapidly restored to the lawn, and put in its 
place, where the turf had been cut out, and in as good contact with the ground 
as possible. The pan and turf were then brought back, the under side of the pan 
carefully cleaned and dried, and all weighed again to make sure nothing was 



16 MR JOHN AITKEN ON DEW. 

lost in the manipulations ; after which it was again restored to its place in 
the lawn, and left exposed while dew was forming. A few experiments were 
made in this way, in all of which the ground was found to lose weight. For 
instance, on the 7th October, the small turf freely exposed to the sky at 
5.15 p.m., when weighed again at 6.30 p.m., was found to have lost 5^ grains 
(0-356 grammes), and by 10.15 p.m. it had lost 24 grains (1*555 grammes). 
Fuller particulars of these experiments will be given further on. 

In making these experiments, the first thing done was to sink two thermo- 
meters in the ground, one to a depth of 3 inches (76 mm.), the other to a depth 
of 1 foot (305 mm.), and to place a third thermometer on the surface of the grass. 
Readings were taken when the experiment began, and again when the pans 
were removed for weighing. During the time the turfs were exposed, generally 
about 5 hours, the soil at 3 inches below the surface lost from 2 to 5 degrees, 
while at 12 inches the loss was small. No doubt part of the heat was lost by 
radiation, but in grass-land, where the surface of the soil is protected by a fairly 
good non-conductor, much of the heat will be spent in evaporating the moisture. 

These experiments prove clearly that under the conditions then existing, 
the soil loses weight, and that vapour really rises from the ground even while 
dew is forming ; therefore the dew then found on the grass must have 
been formed out of the vapour rising from the ground at the time. The dew 
on the grass was, in fact, so much of the rising vapour trapped by the cold 
grass. The blades of grass acted as a kind of condenser, and held back some 
of the vapour which would have escaped into the air. 

It must not be supposed that these experiments in any way contradict the 
well-known observations of Wells and others who have worked at the subject. 
It lias long been the custom to expose different substances to radiation during 
the night, and to estimate the amount of dew on different nights by the increase 
of weight due to the moisture collected on them. It must be noticed that the 
conditions of the two sets of experiments are quite different. In those for 
estimating or measuring the amount of dew, the collecting body must not be 
in heat communication with the earth, an essential condition being that it shall 
receive no heat by conduction from surrounding bodies ; whereas, in the experi- 
ments with the turf, the essential condition is that the body experimented on 
shall be in as good contact with the ground as possible. The result of these 
two conditions is, that in the former, the exposed surface loses heat by radiation 
into space, and soon gets cooled below the temperature of the air, and when 
cooled below the dew-point, dew collects upon it ; while in the latter case the 
exposed surface is in good heat communication with the ground, and tends to 
keep hotter than the other surface ; then being always moist it tends to give off 
vapour, which diffuses away from the hot ground and escapes into the air 
above, but in part is trapped by coming into contact with the cold grass. 



MR JOHN AITKEN ON DEW. 17 

The experiments were generally stopped at night. It would be of no use to 
let them go on till morning, unless one were in attendance at sunrise; for the 
early morning heat radiated from the sun and sky would cause an increased 
evaporation, and make the loss appear too great. On one occasion, however, 
when the morning was dull, weighings were made, and the soil was then found 
to have lost weight during the late night and morning. 

The following simple observation is sufficient to convince us that, under the 
ordinary conditions of our climate, vapour is almost constantly escaping night 
and day from soil under grass. Go out any night, but it is best when terrestrial 
radiation is strong, place one thermometer on the grass, and push another under 
its surface, among the steins, but it need not be into the soil, and note the differ- 
ance in temperature. As an example, I found, at 10.45 p.m. on the 10th October, 
this difference to be as much as 185 degrees. The thermometer on the surface 
of the grass was 24°, while the other, only about 1^ inches underneath it, and 
not in the soil, was as high as 42° 5, the temperature of the air at the time 
being 32° o. Of course, this difference varies, and is not always so great as on 
this occasion, when the sky was clear and the air still. An experiment of this 
kind causes us to doubt the value of the radiation observations made by com- 
paring the readings of a thermometer placed on the grass with the temperature 
of the air in the screen ; because the temperature of the thermometer on the 
grass varies greatly according to its position. If its bulb is supported near the 
tips of the stems, the temperature is much lower than when it is allowed to 
press the grass close to the ground, because in the latter position it receives a 
good deal of heat from the earth. 

It might be objected that these experiments having been made late in the 
year,, and when the soil was damp, they do not prove that evaporation would 
take place in summer when the soil was dry. Other considerations, however, 
lead us to suppose that this nightly evaporation does go on even after a con- 
tinuance of dry weather, though I have no direct experiments to prove it, other 
than those made with the inverted trays. But I find that soil, after it has been 
kept for some time in a house, and when it looks dry and incapable of support- 
ing vegetation, still gives off vapour, and saturates the air over it. This was 
shown by placing over some dry-looking soil a glass receiver, in which was 
hung the hair hygrometer. The instrument soon showed an incease of humidity 
inside the receiver, and after a time indicated saturation. To check the read- 
ing of the hygrometer, it was quickly removed and placed in saturated air, when 
it was not found to change its reading. 

Now as soil, even when it appears dry, tends to give off vapour, and saturate 
the air in contact with it, it is evident that under most conditions of our 
climate the vapour tension at the surface of the ground, amongst the stems of 
the grass, must, owing to the higher temperature, be very much greater than 

VOL. XXXIII. PART I. C 



18 MR JOHN AITKEN ON DEW. 

at the tops of the blades ; and as the air and vapour are warmer, they tend to 
rise and diffuse themselves, and so come into contact with the colder blades at 
the surface, where the moisture gets deposited as dew. 

Having proved that, under the conditions existing during the experiments, 
the ground was giving off vapour during the night, I then proceeded to 
test the value of the observations previously described, and which were made 
by placing shallow trays over the grass, in order to see if those experiments 
were of any value. A small tray, similar to those used in the earlier 
experiments, was prepared. It was made to fit tightly into one of the shallow 
pans, in which, as before, was placed a small turf cut from the lawn. After the 
turf and its pan was weighed, the tray was placed over it, and the whole 
removed, and put in its place in the lawn. This was done at the same time 
as the other experiment previously described, in which the turf and pan, 
after being weighed, was freely exposed to radiation and evaporation. The 
result was that the tray was found to check the evaporation. The inside 
of the covering tray was dewed very much like another one placed over un- 
disturbed grass. The turf covered by the tray lost only 6 grains (0*388 
grammes) during the five hours, or about \ of the amount lost by the one freely 
exposed to the air. This shows that the trays check the evaporation; we may 
therefore conclude that the amount collected by them is less than would be 
given off by the exposed parts of the grass. 

There seems to be reason for supposing that the amount lost per unit of 
area in these experiments, with the freely exposed turfs, is too low an estimate 
for the loss of the lawn at the parts where it was undisturbed, because the 
under sides of the pans were not in good contact with the ground beneath them. 
The experimental turf would not therefore be so warm as the rest of the 
ground, and its evaporation would therefore be less. Most of the heat was 
conveyed upwards towards the experimental turfs by the rising vapour, which 
condensed on the under sides of the pans on which the turfs rested, as they 
were always found to be dripping wet underneath when removed from the soil. 

The question now comes to be, Does this evaporation take place from grass- 
land on all nights and in all weathers ? So far as my observations at present 
go, evaporation is constantly going on, however strong the radiation. On all 
nights on which the inverted trays have been exposed, dew has collected 
on their inner surfaces. There is, however, an indirect way of testing this 
point which may be noticed here, as it is specially applicable to observations on 
giass land. As soil capable of supporting vegetation tends to saturate the air 
in contact with it, it will be admitted that so long as the soil is hotter than the 
air in contact with the grass, vapour will tend to diffuse upwards. Now I find 
1 ij placing a minimum registering thermometer on the grass, and another on the 
top of the soil among the stems of the grass, that there is always a difference 



MR JOHN" AITKEN ON DEW. 19 

between the minimum on and under the grass, often amounting to a considerable 
number of degrees, this difference being greatest on nights when radiation is 
strongest, and least when windy and cloudy. It is only as the day advances 
that the temperature on the grass approaches that under it; this is caused by 
the upper thermometer being heated by solar radiation sooner than the lower ; 
but as the air is by this time drier, there is no tendency for it to lose moisture 
by contact with the colder soil, though some of the dew condensed on the grass 
will, after it evaporates, diffuse downwards, and condense on the soil. It may 
therefore be safely concluded that, on almost all nights in this climate, vapour 
does rise from grass-covered land, and it is this vapour that we see as dew 
on the exposed surfaces of the grass. 

Dew on Soil. 

While the experiments previously described were being made on ground 
covered with grass, parallel ones were made on bare soil. The inverted 
trays placed over soil always showed a greater amount of condensed vapour 
inside them than those over grass. Sometimes there was a heavy deposit 
of clew inside, while there was none outside. This would be owing to the soil 
radiating directly to the trays, and to the amount of heat brought up and con- 
veyed to the trays by the vapour. The temperature of the trays was thus in 
some cases kept above the dew-point of the air outside. 

Experiments were also made by weighing a small area of the surface soil, 
to see if it also lost weight like the grass-land during dewy nights. One of the 
small pans was covered with a thin layer taken from the top of the 
soil. The pan and its soil was then weighed and put on the surface of the 
bare ground at the place where the soil had been taken out. It was left 
exposed the same time as the other trays with the turfs. On weighing, the 
soil was found to have lost 23 grains (1490 grammes) in five hours, or nearly 
the same as the turf. Alongside this pan was placed another one of the 
same area, and with the same weight of soil, but covered with a small tray, 
to see whether the covering trays decreased the evaporation from soil as well as 
from grass. The result was the same as was found with the turf — a decrease 
in the evaporation. The protected soil lost only 8 grains (0'518 grammes). 

The following are the details of a few of the experiments on grass-land and 
on bare soil made on different evenings, and show the temperatures and the 
loss of moisture per 0'25 square foot, or 0023225 square metre, during the 
experiments :* — 

* Throughout this investigation I have adhered to the Fahrenheit scale, as it is the one generally- 
used for meteorological purposes in this country, and because it possesses what appears to me practical 
advantages over the Centigrade scale. The degrees are of a more suitable size, and combine ease in 
reading with accuracy. This scale also avoids a fruitful source of error, experienced by many, when 
taking readings above and below zero. 



20 MR JOHN AITKEN ON DEW. 

October 7, 1885. 5.30 p.m. 

Grass. Soil. 

Temperature of soil, 3 inches below surface, 47°*5 46° 

12 „ h 47°*5 44° 

At 6.30 p.m. 

Grass exposed, lost 5£ grains, or 0*356 grammes. 

M under tray, » 3 h , 194 m 

Bare soil exposed, n 5£ n 0*356 n 

n under tray, n 2f n 0178 m 

At 10.30 p.m. 

Grass. Soil. 

Temperature on surface, 36°*5 40° 

ii of soil, 3 inches below surface, 44° - 5 42°*1 

12 „ „ 47° 44° 

Grass exposed, lost 24 grains, or 1-555 grammes. 

ii under tray, m 6 n 0*388 n 

Soil exposed, .. 23 „ 1-490 

ii under tray, n 8 n 0*518 n 



October 12, 1885. 5.30 p.m. 



Grass. 


Soil. 


44° 


45° 


44°-5 


43-5 


Grass. 


Soil. 


31°*5 


35°*5 


42° 


40°*2 


44° 


43°*5 



Temperature of soil, 3 inches below surface, 
ii n 12 n ii 

At 10.15 p.m. 

Temperature on surface, 

,, of soil, 3 inches below surface, 42 

ii ii ■ 12 ii ii 

Grass exposed, lost 30 grains, or 1*944 grammes. 

n under tray n 6 n 0*388 

Soil exposed, ,. 22 „ 1*425 

n under tray, n 6£ n 0*421 

There was a little wind on this occasion, and very little dew formed. 
During the night the min. on the grass was 28°*5, under it 41°; and it was not 
till 10 o'clock next morning that the thermometer on the grass was as high as 
the one under it. 

The following reading were taken about the 20th October, the exact 
date unfortunately is omitted in note-book : — 

5.15 p.m. 
Temperature of air — Dry bulb, 42*5 ; Wet bulb, 40. 

Grass. Soil. 

Temperature on surface, 39° 42° 

.1 of soil, 3 inches below surface, 46° 48° 

13 i, „ 46°*3 46°-l 



MR JOHN AITKEN ON DEW. 21 

At 10.40 p.m. 

Temperature of air, Dry bulb, 38° Wet bulb, 36° at 4' 0" 

n ii n 33^ ii 33° near ground. 

Grass. Soil. 

Temperature on surface, 31° 34° 

n of soil, 3 inches below surface, 44°-2 43° 

12 ii „ 46° 46° 



Grass exposed, 


lost 


9 grains, or 


- 583 grammes. 


H under tray, 


ii 


8 „ 


0-518 


ii 




Soil exposed, 


ii 


16i - 


1-069 


H 




ii under tray, 


ii 
Next 


9 ,i 

MORNING AT 9 A.M. 


0-583 

Grass. 


n 


Soil. 


Temperature on surface, 




39°-5 




39°-5 


ii of soil, 


3 inches under surface, 42° # 5 




40°-5 


ii ii 


12 


ii n 


45°-5 




45°-5 


Grass exposed, 


lost 


19 grains, or 


1"231 grammes. 


ii under tray, 


It 


13 n 


0-842 


ii 




Soil exposed, 


II 


30 .. 


1-944 


H 




M under tray, 


II 


18 „ 


1-166 


ti 





These figures cannot be supposed to represent anything definite, they 
only indicate a condition of matters which has not been previously observed. 
They show that evaporation in our climate is going on night as well as day 
during dry weather, but the extent to which it takes place cannot be gathered 
from these observations, as they are far too few for the purpose — too few alike 
with regard to seasons, humidities, and exposures ; nor can the proportionate 
amount of evaporation from bare soil and from grass-land be arrived at from 
the weights given. These readings can only be considered true for the place 
and moisture at the time of the year when the experiments were made. For 
instance, the inverted trays over soil in my early experiments always indicated 
a larger evaporation from soil than from grass, while the later ones did not. 
But the early experiments were made over soil freely exposed to sunshine 
during the whole day, while the later ones were made at a place less freely 
exposed, on account of the situation where the first experiments were made 
being too far from the place of weighing. It is evident the amount of sunshine 
will be an important factor in this nightly evaporation, as it will greatly 
determine the amount of heat stored up during the day, and available for 
evaporation during the night. 

I extremely regret the season was so far advanced before these experiments 
were begun, as most of the weather suitable for the purpose was past. I have, 
however, endeavoured to check my results as well as possible. Still I feel that 
what has been done is only preliminary. Similar experiments would require to 



22 MR JOHN AITKEN ON DEW. 

be made during the whole year, to determine whether this evaporation is 
constantly going on or not in fair weather, and to determine its amount 
under different conditions. The varieties of soils, of humidities, and exposures 
are so great that an enormous number of experiments would require to be 
made to determine with any degree of accuracy the amount of evaporation 
that takes place from any large tract of land. 

The temperatures of the soil and of the air during these experiments were 
not high, but we must remember they were taken in October. In summer we 
have to deal with much higher temperatures and greater vapour tensions, and 
therefore the possibilities of heavier dews. On the 18th August I find the 
temperature \ inch under the surface of the soil at 4 p.m. was 82°, at 3 inches 
underneath it was 72°, the temperature of the air being 66°. At 9 p.m., at 3 
inches deep, the temperature was 60° under grass and under bare soil. The 
temperature on the grass was 45°, while a thermometer placed on bare soil 
was 52°. Next morning the temperature at 3 inches under grass was 56°, 
and at the same depth under soil 52°. The soil at 3 inches down had thus lost 
20 degrees during the night, and that nearer the surface would have lost a 
good deal more. Much of this loss would be spent in evaporating moisture. 
On this occasion it will be noticed that at night the difference between the 
temperature on the surface of the grass and on the bare soil was as much as 
7 degrees, and this easily explains why the ground kept dry while the grass 
got wet. 

So far as my limited observations go, evaporation is constantly going on 
from soil under grass, but on a few occasions it was doubtful whether the reverse 
process had not taken place, and vapour got condensed on the surface of bare 
soil. On one or two occasions in autumn, I observed soil which had been dry 
the previous day to be damp in the morning. The soil had evidently received 
an increase of moisture. But the question still remains, Whence this 
moisture ? Came it from the air, or from the soil underneath ? The latter 
seems the more probable source, as the higher temperature below would 
determine a movement of the moisture upwards by the vapour diffusing ; and 
the surface soil being cold, the vapour would be trapped by it before it escaped 
into the air, in the same way as it is trapped by grass on grass land. 

•During summer it is difficult to trace the vapour condensed on the surface 
of the soil to its source, and to say definitely whether it came from the air or 
from the ground underneath. But on the morning of the 12th October I had 
an interesting opportunity of studying this question. During the night the 
radiation had been very powerful, the surface of the soil was greatly cooled, 
and a thin crust of frozen earth formed. After the sun had thawed the sur- 
face it was very wet. An examination of the soil before the sun had acted on 
it, showed that the vapour condensed near its surface had come from under- 



MR JOHN AITKEN ON DEW. 23 

neatli. On lifting the small clods on the surface, it was observed that their 
under surfaces and sides, when close to each other, were all thickly covered 
with hoar-frost so thickly as to be nearly white, while the upper surfaces 
exposed to the passing air had but little deposited on them, — the interpreta- 
tion of which seems to be, that the vapour rising from the hot soil underneath 
had got trapped in its passage through the cold clods. Its presence under- 
neath and on the sides of the clods was an evidence that the moisture was 
on its passage from the ground, when it met with the cold surface which im- 
prisoned it. 

This hoar-frost on the sides and under the clods could not be due to vapour 
condensed from the passing air, because the upper surfaces of the clods had 
scarcely any deposited on them, and that in spite of the fact that the upper 
surfaces would be the colder, as they were those from which the radiation 
was taking place. It seems probable that even the vapour condensed on the 
upper surfaces of the clods was part of the vapour escaping from the soil, and 
was not taken from the passing air. 

The occasions when the earth is most likely to receive vapour condensed 
upon it from the passing air, are not on clear nights when the radiation is 
strong, but rather when after strong radiation and cooling of the surface 
the weather changes, becomes cloudy, and a warm moist wind blows over the 
land. Occasions of this kind are seen most frequently after frosts, and 
undoubtedly much moisture is then condensed on the soil, but the moisture 
so condensed is not what we call dew. 

Dew on Koads. 

There is considerable difference among works on dew as to the absence 
of dew on roads, but almost all agree in stating that it is never formed on 
roads ; and the presence of dew on grass, while none is visible on roads, is 
generally attributed to the greater radiating power of vegetation over that of 
the material of which our roads are composed. Now I find that this state- 
ment as to facts is wrong, and the explanation is also inaccurate. Dew really 
does form on roads in great abundance on dewy nights, and the material of 
the road is practically as good a radiator as the grass. 

The reason why it is generally saicl that dew is not seen on roads is 
owing, not to the less radiating power of the stones, but to the fact that dew 
has not been looked for at the proper place. The blades of grass are practi- 
cally non-conductors of heat, while stones conduct fairly well. The result of 
this is that we are not entitled to look for dew on the upper surfaces of stones, 
as on grass, but it must be sought for on their under sides, because the stones 
are good conductors, and the vapour tension under them is much higher than 
at their upper surfaces, owing to the higher temperature of the air laden with 



24 MR JOHN AITKEN ON DEW. 

moisture rising from the ground. If we examine a gravel walk on a dewy 
evening, we shall find the under sides of the stones, especially those near the 
solid ground, to be dripping wet; and we may occasionally see isolated patches 
of stones wet on the upper surface, probably due to an openness in the ground 
at the place permitting a free escape of vapour. 

Another reason why the upper surface of the gravel does not get wet, is 
that it is in good heat communication with the ground; the stones are thus 
kept warm; and as a good deal of the vapour rising from the ground is trapped 
by the under surfaces of the stones, the vapour which escapes these surfaces is 
not enough to saturate the air at the temperature of the exposed surfaces of 
the gravel. The following temperature, taken at 10 p.m. on the 25th September, 
will give an idea of the difference in temperature on the surface of grass and 
on gravel, and show why no dew is formed on the top of the stones while it 
collects on the grass. A thermometer placed on the surface of the gravel was 
34°, while one placed near it, but on grass, was 30°, or 4° lower. At the 
surface of the soil under the grass the temperature was 40°, and it was almost 
exactly the same temperature at the bottom of the gravel which was 1\ inches 
deep. 

We see from the above that hot vapour, rising from the ground under 
grass, ascends till it comes into contact with the cold blades, and is condensed 
on their exposed surfaces; whereas on the gravel road the under sides of the 
stones are nearly as cold as their exposed surfaces, and much of the warm 
vapour gets condensed under them, while the vapour which escapes to the 
surfaces has its dew-point lowered by mixing with the surrounding air, and 
the upper surfaces of the stones being in good heat communication with the 
ground, are not cool enough to condense this vapour and form dew. 

A simple manner of studying the formation of dew on roads is to take, say, 
two slates, and place one of them on the gravel and one on a hard part of the 
road. If these slates are examined on a dewy night, their under sides will be 
found to be dripping wet, though their upper surfaces and the road all round 
them are quite dry. This experiment also shows us that under most conditions 
of our climate vapour does rise from hard dry-looking roads on dewy nights. 

In studying questions of this kind, and for showing the importance of the 
heat communicated by the earth to the radiating body, the following experiment 
may be useful. Place on the grass, soil, or road, a slate and a piece of iron, 
say an ordinary 7 lb. weight. Alongside of these place another slate and 
weight; but instead of the latter resting on the ground, elevate them a few 
inches on small wooden pegs driven into the earth. If we examine the 
surfaces of these bodies on dewy nights, the following will be the general 
result. While the grass all round is wet with dew, we shall find that the 
upper surfaces of the slate and the weight resting on the ground keep dry, and 



MR JOHN AITKEN ON DEW. 25 

those of the elevated ones get wet like the grass, the reason for this is that the 
bodies on the ground as well as the elevated ones are constantly losing more heat 
by radiation than they receive by absorption ; but those in contact with the 
ground have heat communicated to them by conduction and by the condensa- 
tion of vapour on their under surfaces; their temperature is thus prevented 
from falling as low as that of the elevated bodies, which only receive heat 
from the passing air ; the latter are thus cooled more by radiation than those 
on the ground. Bodies out of heat communication with the ground thus tend 
to cool more than those in contact with it; and while the former get cooled 
below the dew-point and collect dew, the latter keep warmer than the dew- 
point, and thus tend to keep dry, or if wetted to become dry again. 

These considerations suggest a simple method of testing whether the surface 
of any particular part of the ground is giving off vapour or not. It is very 
evident that so long as the temperature of the surface of the soil is above the 
dew-point of the air, vapour will rise from the ground, and that if the 
surface is cooled by radiation below the dew-point, evaporation will cease, 
and vapour will condense upon it. In order to test this, all that is necessary is 
to place on the ground, and in good heat communication with it, some substance 
that is a good conductor, and shows dewing easily. A piece of metal 
covered with black varnish does well. It is painted black, not in order to radiate 
copiously, but because black shows any deposit of dew most quickly and easily. 
So long as this test surface keeps dry while in contact with the ground, the 
soil round it must be giving off vapour, because the temperature of its surface 
is higher than the dew-point. But if the temperature of the ground falls 
below the dew-point it will collect moisture, and this test surface will 
collect dew also, and will thus tell us that the surrounding soil is receiving 
moisture. In experiments such as these we are simply converting a small 
area of the earth's surface into a condescending hygroscope, and our test 
surface tells us whether the earth's surface at the place is cooled by radiation 
below the dew-point or not. So long as no dew forms on the test surface 
vapour is being given off. 

These test surfaces must not be large, at most only two or three centimetres, 
because if large they would check the free passage of the vapour to the air, 
and so prevent the soil under them from cooling to the same amount as the 
surrounding ground ; and further, it is difficult to get good contact with large 
surfaces, without which only a part of the test surface keeps clear, while 
the part not in contact gets dewed, even though the temperature of the surface 
of the ground is above the dew-point. This was confirmed by observations 
made on a frosty night. On lifting each test plate, it was observed that the 
soil was frozen to it under the clear parts, and no soil adhered under the parts 
that were dewed. In my experiments I have used small copper discs covered 

VOL. XXXIII. PART I. D 



26 MR JOHN A1TKEN ON DEW. 

with black varnish, ordinary glass mirrors, and also small black mirrors, in 
order to get rid of the objection to ordinary silvered mirrors, namely, that they 
might not be good radiators. On no occasion up to the beginning of November 
have I yet seen dew on any of these at night, but it is difficult to say whether 
dew had not formed on them on some mornings, as the air was thick and 
misty, and the deposit then observed might have fallen as fine rain. 

The changes in temperature of the surface of the soil clue to radiation, give 
rise to a downward movement of heat during the day, and to an upward move- 
ment of it during the night. These heat changes will be accompanied by 
corresponding movements of the moisture in the soil. During day, after the 
surface is heated, the vapour tension being higher above than below, a 
downward movement of moisture will take place ; and at night this process 
will be reversed, the tension of the vapour at a depth being greater than near 
the surface, the vapour rises and condenses in the colder soil. Part of the 
latent heat so liberated by the rising vapour is spent in radiation from the 
surface, part in evaporating moisture, and a little in heating the air cooled by 
contact with cold grass, &c. 

We may conclude that, owing to the heat received during the day, and 
probably also to the internal heat of the earth, vapour continues to rise from 
the ground long after the sun has set, and in many conditions the vapour 
continues to rise the whole night; but under certain others it seems probable 
that the reverse will occasionally take place, and vapour condense on the 
ground. This is most likely to take place soonest on bare soil, especially on 
those parts of it that are in bad heat communication with the ground under- 
neath. But over grass-land in most conditions of our climate, when dew is 
forming, the evaporation seldom seems to stop, but goes on night and day, on 
account of the surface of the soil being protected by the grass from losing its 
heat so quickly as the bare soil. The escaping vapour rises till it meets with 
some surface not in good heat communication with the ground, and which has 
been cooled by radiation, in the manner set forth by Wells and others. 
These remarks refer to weather when dew is most abundant, as in spring, 
summer, and autumn, and do not apply to those conditions in which a warm 
vapour-laden air is brought over a cold ground. 

Dew and Wind. 

It is well known that during windy nights no dew is formed. We pre- 
viously knew that wind acts in two ways to prevent the formation of dew; 
to these two ways we must now add a third. Wind prevents the formation of 
dew — (1) by mixing the hot air above the surface of the ground with the air 
cooled near its surface, this tends to prevent the air being cooled to the dew- 



MR JOHN AITKEN ON DEW. 27 

point; (2) the wind by its passage over the surface of radiating bodies 
prevents these surfaces being cooled much below the temperature of the air; 
the wind thus tends to prevent the air in contact with these surfaces being 
cooled below the dew-point ; and (3) wind blowing over the surface of the 
ground rapidly carries away the vapour rising from the soil, and mixes it up 
with a large quantity of drier air. The wind thus tends to prevent an 
accumulation of clamp air near the ground. 

To illustrate this third effect of wind, let us use the observations made on 
the evening of October 12. The sky was clear, and there was a considerable 
amount of radiation, but a slight wind was blowing. The bare soil in the test- 
pan lost 22 grains and the corresponding turf lost 30 grains in about five hours. 
Almost no dew was formed on the grass, but trays placed over the bare soil 
and over grass had their inside surfaces covered with moisture, though not so 
heavily as was generally observed on dewy nights. The reason why so little 
clew formed on this occasion was, partly, that the wind prevented the tempera- 
ture of the air near the ground falling as much as it would have clone if it had 
been calm. In the screen the temperature only fell to 40°. On the grass, 
however, it fell to 31°*5, and on the soil to 35° "5; but a good deal depended on 
the exposure of the thermometer to the wind. From the above we see that, 
though wind was blowing, the thermometer on the grass fell a good deal below 
the temperature of the air, and showed a considerable amount of radiation. The 
wind apparently prevented the formation of clew on this occasion, principally by 
preventing an accumulation of moist air near the surface of the ground. The 
inverted trays showed that if the wind had fallen dew would have formed, 
because it formed in the still air under the trays. The deposit was not so heavy 
inside the trays on this occasion as was often seen in dewy nights, because the 
wind prevented the radiation cooling the top of the trays to the same extent as 
when it was calm. 

Dew and Vegetation. 

When I began to make observations on dew, one of the first things I did 
was to make a tour of the garden on a dewy night, and to examine the 
appearance of the plants. A very short survey was sufficient to show that 
something else was at work than radiation and condensation to produce the 
effects then seen. Let me briefly describe what I saw, and what at once 
struck me could not be explained by the ordinary laws of radiation and con- 
densation. Certain kinds of plants were found to be covered with moisture, 
while others were dry. Many plants of the Brassica family were heavily 
covered with glistening drops; while beans, peas, &c, growing alongside them, 
were quite dry. Again, in clusters of plants of the same kind some were wet, 
while others were not; and not only so, but some branches were wet, while 



28 MR JOHN AITKEN ON DEW. 

others on the same plant were dry. These differences were noticed to be quite 
irrespective either of their exposure to the sky, or to the probable humidity of 
the air surrounding them. 

In illustration of this latter point, small clusters of dwarf French poppies 
may be mentioned. Most of the plants were quite dry, whilst others growing 
amongst them were dripping with moisture; and while some branches were 
dry, others on the same plant were studded with drops, and the general 
surface of the leaves in some cases wet. On examination of these plants 
next day, it was observed that those that were wet at night were all plants 
in vigorous growth, and the shoots that were dewed were those in which the 
vegetation seemed most active. It was also observed that it was always the 
same plants and branches that were dewed night after night during the 
short time the observations were made. 

A closer examination of the leaves of broccoli plants showed better than 
any others that the moisture collected on them was not deposited in the 
manner we should expect if it had been deposited as an effect and according 
to the laws of radiation ; nor was it deposited in accordance with the laws of 
condensation; indeed, every appearance was at variance with these laws. 
Examination showed that the moisture was collected in little drops placed at 
short distances apart, along the very edge of the leaf, while the rest of the leaf 
was often dry. Now, if the moisture had been condensed by cold produced by 
radiation, then it would have been most abundant on the upper surface of the 
leaf; but there would have been none on its windward edge. This is well 
seen when we expose a small glass plate on a dewy night; the windward edge 
is always dry, and the deposit is spread evenly over the rest of the plate up to 
the opposite margin, because the temperature of the air when it first strikes 
the plate is higher than the dew-point, and it has to travel over more or less 
of the surface of the glass before it is cooled enough to deposit its moisture. 
Again, if these drops on the edge of the leaf had been deposited according to 
the laws of condensation, then the moisture would have been deposited on the 
surface more in accordance with the distribution of temperature at the different 
points; the moisture would therefore have been more equally distributed, and 
not been in large isolated drops. 

On further examining these plants, I placed the lantern behind the blade, and 
then observed that the position of the beautiful sparkling diamond-like drops 
that fringed its edge had a definite relation to the structure of the leaf; they 
were all placed at the points where the nearly colourless and semi-transparent 
veins of the leaf came to the outer edge, at once suggesting that these veins 
were the channels from which the drops had been expelled. 

These isolated drops on the edges of the leaves were therefore evidently 
not dew, but an effect of the vitality of the plants. An examination of grass 



MR JOHN AITKEN ON DEW. 29 

blades showed that they also tend to have large drops t attached to them, 
while the rest of the blade is dry, and these drops were always found, to be 
situated at certain definite points; they were always near the tips of the blades. 
These large drops seen on plants at night are therefore not dew at all, but are 
watery juices exuded by the plants. 

Now this excretion of water by the leaves of growing plants is not a new 
discovery — it has been long well known. But what seems extremely curious is, 
that its relation to dew has never been recognised, at least so far as I am 
aware, and. it must be admitted that it is one of considerable importance. 

It is well known that plants transpire from their leaves an immense amount 
of moisture, which passes off in an invisible form. Prof. J. Boussingault found 
that mint transpired 82 grammes of water per square metre in sunshine, and 
36 grammes in shade; but if the roots of the plants were removed, they only 
transpired 16 and 15 grammes respectively. This simple experiment proves 
that the root sends into the stem of the plant a supply of water, that it acts as 
a kind of force-pump, and keeps up a pressure inside the tissues of the plant. 
This supply sent in by the root is in most conditions removed by means of 
transpiration from the surface of the leaves. 

Now what will be the result if transpiration is checked, while the root con- 
tinues to send forward supplies? It will evidently depend on two things — 
first, the pressure the root is capable of exerting before its action is stopped; 
and second, the freeness with which the water can escape from the leaves. If 
the root pressure is small, it will cease with the transpiration ; but if it is great, 
the sap will be forced into the plant, and if nature has provided any outlets it 
will escape at these openings. 

Dr J. W. Mool* has given great attention to the subject, and has experi- 
mented on a number of plants. The method he employed in his researches 
was to place the leaves under the most favourable conditions for the excretion 
of drops, by diminishing the transpiration as far as possible, and by supplying 
them with water. He substituted for root pressure, a pressure produced by a 
column of mercury. Out of 60 plants experimented on by Dr Mool, he found 
that the leaves of 29 excreted drops without being injected, 13 leaves became 
injected and excreted drops, and 18 became injected and did not excrete at 
all. He says that the excretion takes place by water-pores, and by ordinary 
stomata, while in some cases it occurs at surfaces possessing neither of 
these organs. 

I have recently made a few experiments on this subject in its relation to 
dew. As, however, the season was far advanced before the experiments were 
begun, but little could be accomplished, for the activity of the plants was nearly 
over, and grass was almost the only plant possessing sufficient vitality for 

* Nature, vol. xxii. p. 403. 



30 MR JOHN AITKEN ON DEW. 

experimenting. I however removed a branch of the poppy, which, during 
summer, had shown such a tendency to exude moisture, and connected it by 
means of an india-rubber tube with a head of water of about one metre. 
After placing a glass receiver over it, so as to check evaporation, it was left for 
two or three hours, when it was found to have excreted water freely — some 
parts of the leaves being quite wet, while drops had collected at other places. 

The broccoli plants which had excited my interest in summer were also 
experimented with. A full-grown leaf was fitted into the apparatus, and the 
pressure applied. In a little over an hour it also exuded water, and soon got 
fringed with drops along its edge in exactly the same way that was observed on 
it in summer. Another leaf from the same plant, but much younger, being 
about one quarter grown, on being tested in the same way did not excrete at all, 
after the pressure had been applied for twenty-four hours. Here we have the 
same result as that noticed in summer — one leaf exudes, while another on 
the same plant does not. 

If the water pressed into the leaf is coloured with aniline blue, the drops 
when they first appear are colourless, but before they grow to any size, the 
blue appears, showing that little water was held in the veins, but the whole 
leaf got coloured of a fine deep blue-green, like that seen when vegetation is 
very rank, showing that the injected liquid had penetrated through the 
whole leaf. 

Most of my experiments on this subject were made with grass. I find 
that even in the middle of October, after having been severely frosted two or 
three times, which had probably reduced its vitality, it still exuded so abun- 
dantly that drops collected in air which was not saturated. A turf placed in 
a cellar, dry enough to keep glass quite free from dewy deposit, soon collected 
drops. These drops always appear near the tips of the blades ; they are not 
exuded from every blade, and sometimes from only one on each stalk, but 
generally from more ; and it is always from the blades that seem to have the 
greatest vitality, and are nearly, but not quite full grown. Sometimes it is the 
youngest blade that exudes, but if it is very small, it is the second youngest. 
As the blades grow old they cease to exude ; but this seems to be due to 
some change in the blade at the point where it exuded, and not to a diminution 
of root pressure, as it exudes freely when the tip is cut off. 

The question might be here raised, Are these drops really exuded by the 
plant \ Are they not due to some condensing power possessed by the leaves, 
by the presence at these points of some substance possessing an affinity for 
water vapour, or some process by which they may extract moisture from the 
air ? To get an answer to this question, I selected a small turf, placed 
over it a glass receiver, and left it till drops were excreted. Removing 
the receiver, a blade having a drop attached to it was selected. After being 



MR JOHN AITKEN ON DEW. 31 

carefully dried, the tip of the blade was placed in a small glass receiver, so 
as to isolate it from the damp air of the larger receiver. This small 
covering glass measured about 10 mm. in diameter by about 15 mm. in 
height. Its open end was closed by means of a very thin plate of metal 
cemented to it. In the centre of this plate was pierced a small opening, of 
the same size and shape as the selected blade of grass. The tip of the blade 
was entered about 5 mm. into this small receiver, and to prevent moisture 
entering and coming in contact with the tip of the blade, an air-tight joint between 
the blade and the metal was made with india-rubber solution. The tip of 
the blade was thus isolated inside the small receiver in which the air was 
dry. The large glass receiver was then placed over the turf to prevent 
evaporation from the lower part of the blade, or the experiment was made in a 
room where the air was not very dry. After a time, generally some hours, the 
turf was examined. A drop was always found to have formed on the tip of 
the blade inside the small receiver, and this drop was, as nearly as could be 
judged, always as large as the drops formed in the moist air under the large 
receiver. It would thus appear that these drops are really exuded by the 
plant, and not extracted from the air. 

These exuded drops seem to be almost entirely the result of root pressure, 
because if we cut off the roots, and place the stems in water, putting over all 
a glass receiver standing in water so as to saturate the air, and as a test 
that the conditions are favourable, placing a small turf alongside the 
cut grass under the receiver, we shall find that scarcely any drops make 
their appearance on the rootless stems, while those with roots have drops 
attached to them. Again, if we take one of these rootless stems, and attach it 
by means of the india-rubber tube to a head of water, it is found to exude 
drops at the tips of its blades in moist air in the same way as when it was 
attached to its roots. 

These excreted drops are formed on grass on other than dewy nights. 
After rain, if there has been no wind, and the air near the ground becomes 
saturated, a rearrangement of the drops takes place. Some time after the rain 
has ceased, most of the blades will be found to be tipped with a drop at the 
same point as the exuded drop appeared at night — a position which no falling 
rain drop could keep. This tendency of plants to exude moisture explains 
why the grass is almost always wet during autumn. At that season evapora- 
tion is slow, and as the plants are constantly pouring in supplies to the drops, 
it takes a long time for the slow evaporation to overcome the wetting effect 
and dry up the grass. 

The question as to what degree of humidity in the air is necessary before 
plants will exude drops, would seem to be greatly determined by the rate at 
which the supply is sent into the leaf. If the supply is greater than the 



32 MR JOHN AITKEN ON DEW. 

evaporation from the whole surface of the leaf, the drop grows ; but if the 
supply is less, it does not form, or if formed, it decreases in size. The rate of 
the supply will evidently depend on the kind of plant and the amount of its 
vital activity at the time. The formation of drops on plants that exude 
moisture will therefore depend on the rate of supply, the humidity of the air, 
and the velocity of the wind. It is not easy to get a satisfactory experimental 
answer to this question, on account of the soil near the grass tending to 
moisten the air over it. A small turf placed in an elevated position in the 
centre of a room has been observed to have drops on it, when there was a 
difference of more than one degree between the wet and the dry bulb thermo- 
meter hung alongside. As the drops are exuded at the tips of the blades, 
it is probable the air in contact with them was not much moistened by the 
small area of soil underneath. 

These observations entirely do away with the explanation usually given of 
the tendency of grass to get wet early and heavily on dewy nights. It has 
generally been explained by saying that grass is a better radiator than most 
substances, and therefore cools more, and sooner, than other bodies. We 
now see that those drops that first make their appearance on grass are not 
drops of dew at all, and their appearance depends, not on the laws of dew, but 
on those of vegetation. Hence the varied distribution of moisture on plants 
and shrubs on dewy nights. 

We have seen that much of the moisture that collects on plants at night 
does not form like dew on dead matter. Dead matter gets equally wet where 
equally exposed, and the moisture does not collect on it in isolated drops, as 
it does on plants. Those drops which appear on grass on clear nights are not 
dew, and they make their appearance on surfaces that are not cooled to the 
dew-point. If the radiation effect continues after these drops have been 
forming for some time, true dew makes its appearance, and now the 
plants get wet all over their exposed surfaces in the same manner as dead 
matter. This latter form of wetting or true dew is of rarer occurrence than 
we might at first imagine. On many nights on which grass gets wet, no true 
dew is deposited on it; and on all nights, when vegetation is active, the exuded 
drops always make their appearance before the true dew ; so that when we 
walk in early evening over the wet lawn, it is not dew that we brush off the 
grass with our feet, but the sap exuded by the plant itself. The difference 
between these exuded drops and true clew can be detected at a glance. The 
moisture exuded by grass is always excreted at a point situated near the tip 
of the blade, and forms a drop of some size, which may form while the rest 
of the blade is dry, but true dew collects evenly all over the blade. The 
exuded liquid forms a large glistening diamond-like drop, whereas dew coats 
the blade with a fine pearly lustre. 



MR JOHN AITKEN ON DEW. 33 

I feel that the dissecting hand of science has here dope an injury to our 
poetic feelings. Every poet who has sung of the beauties of nature has added 
his tribute to the sparkling dew-drop, and Ballantine in his widely-known 
song has taught a comforting lesson from the thought that " ilka blade o' grass 
keps its ain drap o' clew." No doubt the drop of clew to which the poets refer 
is the large sparkling diamoncl-like gem that tips the blades of grass, and which 
we now know is not dew at all. While, however, our interpretation of nature 
has changed, the teaching of the poet remains, and the sparkling dew-drop may 
still teach the same comforting lesson. We must, however, change our views 
regarding the source of the refreshing influence. We may no longer look upon 
it as showered down from without, but as welling up from within — no longer as 
taken by the chill hand of night and given to refresh and invigorate exhausted 
nature ; we must rather look upon it as suggesting that we are provided with 
an internal vitality more than sufficient to restore our exhausted powers, after 
the heat and toil of the clay are past. 

Radiation. 

I have said in a previous part of this paper that the surface of bare soil and 
of roads will radiate at night as much heat as grass. It may be thought I have 
said this simply because we do not now require that grass should be the more 
powerful radiator to enable us to explain its greater wetness on dewy nights. 
Though it is not now necessary to suppose that grass is a powerful radiator, yet 
there is nothing in the above experiments to prove it either a good or a bad one. 
It therefore seemed desirable that some definite experiments be made on this 
point, and also to determine the radiating powers of different substances at 
night, as this is always an interesting and important point in questions con- 
nected with the deposition of dew ; and the radiating power of grass, though 
not the principal cause of its wetness at night, might be still considered to play 
a subordinate part. 

We have already a great number of experiments on the radiating powers of 
different substances. Unfortunately most of the accurate measurements of this 
kind are from laboratory experiments, and do not appear to bear very directly 
on our subject. Franklin's early experiments, made with different coloured 
cloths placed on snow, seem to have given our ideas an unfortunate bias on 
this subject. From observing the different depths to which cloths of dif- 
ferent colours sunk in snow, when exposed to solar radiation, he came to 
the conclusion that the dark colours absorb most heat, and this conclu- 
sion seems for long to have influenced our ideas. If the heat radiated and 
absorbed by a surface was composed entirely of visible rays, then no doubt 
the colour of a body would be an index of its radiating and absorbing powers. 

VOL. XXXIII. PART I. E 



34 MR JOHN AITKEN ON DEW. 

But os the eye gives us no information about the greater proportion of the 
radiant energy, its indications are of no value in determining the radiating and 
absorbing powers of different surfaces. 

Experiment shows that different surfaces have different absorbing powers 
for different rays. Melloni, for instance, found that white lead absorbed only 
about half as much heat from a Locatelli lamp as lamp black did, while it 
absorbed as much as lamp black when the source of heat was copper at 100° C. 
It is evident from this, that we cannot take the result of experiments made in 
the laboratory, and apply them to surfaces exposed to the temperature of 
the sky on a clear night. It may be possible that the radiating and 
absorbing powers of different surfaces may bear the same proportion to each 
other when the temperature is 0°, and they radiate into space, as when their 
temperature is 100°, and they are exposed to surfaces at the ordinary tem- 
perature of the laboratory. This may be so, but till it is proved we can- 
not apply these laboratory experiments to the cooling effect of radiation at 
night. 

Some experiments on the radiating power of different substances exposed 
to a clear sky were made by Daniell. He used for his purpose two similar 
parabolic reflectors. In the focus of each was placed the bulb of a ther- 
mometer. In experimenting he turned the reflectors to the sky, and coated 
the bulbs of the thermometers with the substances to be tested. Comparing 
garden mould with black wool, his measurements show, from the average of 
three readings given by him, that while the black wool fell 9° below the 
temperature of the air, the mould fell only 6°. The difference between the 
radiating powers of chalk and black wool, as given by him, was not quite so 
great. There seems to be an objection to this method of experimenting. 
The different surfaces here lose more heat by radiation into space than they 
receive. To supply this loss, they receive more heat by radiation from the 
reflector than they give, and they also receive heat from the surrounding air, 
conveyed to them by connection currents. Now in the experiment as arranged 
by Daniell, the two surfaces will not receive the same amount of heat from 
the latter source. The wool surface will not have such a free circulation of air 
over it as the other one ; it will therefore not receive so much heat, and its 
temperature will thus tend to fall lower. 

It appeared that something more might be done in this direction, and on con- 
sideration it was thought that the radiation thermometers, described by me in 
a previous paper, might be suitable for the purpose. It may be remembered 
that the principle on which these radiation thermometers is constructed is, 
that a large surface is more highly heated than a small one by radiation during 
the day, on account of the absorbed heat being more slowly taken away by 
the passing air from the former than from the latter ; and for a similar reason 



MR JOHN AITKEN ON DEW. 35 

a large surface is colder at night than a small one, as the small surface receives 
more heat, per unit of area, from the air than the large one. The absorbing 
and radiating surface of these instruments is a large flat area, painted black, 
and its temperature is taken by means of a thermometer, with its bulb placed 
under the centre of the radiating surface."' 

The construction of these radiation instruments has been altered, and those 
used in this investigation were made of metal in place of wood, as described in 
the previous paper, the radiating surface being a thin plate of metal, 14 inches 
(355 mm.) square. A thin metal tube is fixed close to and parallel with the 
under surface of the plate. One end of the tube terminates at the centre 
of the plate, and the other at the edge. The thermometer is placed in 
this tube with its bulb under the centre of the plate, and to prevent heat 
escaping or being absorbed at the back, a considerable thickness of cotton wool 
is placed under it. The instrument is practically a shallow box, 14 inches 
square by 2 inches (51 mm.) deep, packed with cotton wool. One of the 
flat areas of the box is exposed to radiation, and its temperature is taken by 
means of a thermometer placed under its surface. In the following I shall 
refer to this instrument simply as the thermometer box. 

One of the advantages of this form of instrument for solar radiation 
experiments is, that the readings given by different instruments agree with 
each other, at least this is the case so far as my experience goes; and it is well 
known that the vacuum radiation thermometers are unsatisfactory in this 
respect, no two almost ever reading alike. For instance, the vacuum 
radiation thermometers used at the Indian Stations, when compared with 
another of the same pattern as standard, were in some cases found to 
differ as much as 15°, though they were exact copies of each other, and 
similarly exposed.t I find that when the different instruments of the kind 
used by me are compared they agree very well when of the same size. It is of 
course necessary that they be of the same size — this results from the principle 
of their construction. It seems possible that we might make boxes of different 
sizes, and from them determine the law of variation for size; so that, knowing 
the size of the surface used in any particular set of observations, we could 
determine what temperature its readings corresponded to in another instrument 
of a different size, or all readings might be reduced to a standard size, say the 
temperature of a very large surface. 

I may mention that the temperature given by an instrument of the size 
here described when placed in sunshine is a good deal above that indicated 
by a vacuum thermometer, which had been carefully prepared for me by 
Casella of London. Generally the readings were about 12 per cent, higher. 

* Thermometer Screens, Proceedings of the Royal Society, Edinburgh, No. 117, 1883-84. 
t Report of the Meteorology of India, 1879, hy H. P. Blanford, E.R.S. 



36 MR JOHN AITKEN ON DEW. 

One objection to these large-surface radiation thermometers is that they are 
more affected by wind than the vacuum ones. If it is a question of solar 
energy we are considering, this certainly is an objection, but if it is one of 
climate it will scarcely be so. I need not say that for questions of terrestrial 
radiation at night the vacuum thermometer is of no use. 

In using these thermometer boxes for determining the radiating powers of 
different surfaces at night the following method was employed : — Two precisely 
similar boxes were prepared, and their upper surfaces painted black. They 
were placed in an elevated position in the open air, commanding a clear 
view of the sky all round. They were first exposed without anything on their 
surfaces, to see if their readings were exactly alike. In constructing them care 
was taken to put the same amount of cotton wool in each, in order that their 
non-conducting powers and heat capacities might be the same, so that both 
might take the same amount of heat to warm them, and both lose the same 
amount of heat at the back. On trial both instruments were found to read 
alike wheu similarly exposed. 

As the sky radiation is a rather variable quantity, it would not do, on most 
nights, to leave one of these test surfaces bare, and use it as a standard with 
which to compare the other, over which we have put the substance to be 
tested, because the uncovered surface will follow the changes in the radiation 
more easily than the other, and will change more, and sooner, than the 
one covered with the substance to be tested, particularly if the substance is 
a bad conductor. The method generally adopted was to place both surfaces as 
nearly as possible under the same conditions. For instance, the first substances 
tested were black and white cloths of different materials; of each kind a black 
and a white was selected, each pair being as much alike as possible, of the 
same material, of the same weight, and of the same texture. A black one 
was placed over one thermometer box, and the corresponding white one 
over the other. After a time the readings were taken, and the position of 
the cloths reversed, the black being placed over the box where the white 
was, and vice versa, and readings again taken. Then if radiation remained 
constant one of the cloths was removed, and the other compared with the 
black surface. 

The following table shows the results of some experiments made on the 
radiating power of black and white cloths tried in this way. The readings 
were taken on the evening of the 14th November. The sky on the occasion 
was quite cloudless. The air was very dry, and had scarcely any movement — 
an unusually favourable condition for conducting experiments of this kind. 
The radiating surfaces were placed at a height of about one metre from the 
ground, and a protected thermometer for taking the temperature of the air was 
placed alongside at the same height. 



MR JOHN AITKEN ON DEW. 



37 



Air. 


Substance. 


Radiation. 


Substance. 


Radiation. 


35° 


No. 1, black 


28° 


No. 1, white 


28° 


35° 


„ white 


28°'5 


„ black 


28°-5 


35°-5 


j» jj 


28°-5 


» » 


28°-5 


35°-5 


Paint black 


28°-5 


>> jj 


28°-5 


36° 


No. 1, black 


28°-5 


Paint black 


28°-5 


36° 


No. 2, „ 


29° 


No. 2, white 


29° 


35° 


W 3> 


29°-2 


;) i) 


29°-3 


35° 


„ white 


29° 


„ black 


29° 


35°-5 


>> » 


28°'7 


>) >i 


28°-8 


35°-5 


a >> 


28° 


Paint „ 


28° 


35° 


No. 3, white 


27° 


No. 3, black 


27° 


35° 


„ black 


27° 


„ white 


27° 


34°-5 


Paint „ 


26°-5 


J* ?j 


26°-5 


34°-5 


jj » 


26°-5 


>> >> 


26°-5 



In the above table, the first column shows the temperature of the air at the 
height of the radiating surfaces. In the second and fourth columns are the 
substances whose radiating powers are compared, No. 1 being black and 
white cotton cloths, No. 2 merino cloths, and No. 3 thick woollen cloths. 
In the third and fifth columns are the temperatures of the radiating surfaces. 
The following was the manner of conducting the experiments : — Take the first 
on the table. A black cotton cloth was spread over one thermometer box, 
and a white cotton one over the other; after a time, when the readings were 
taken, the temperature of the air was 35°, the black cloth 28°, and the white 
one 28°. The black cotton was now removed from its box, the white one 
put in its place, and the black one where the white one previously was. This 
was done to check any error from difference of exposure to wind or difference 
in thermometer boxes. After a time the readings were taken, and found to 
be— air 35°, white cotton 28*5, and black cotton 28 - 5. The radiation of the cloth 
was then compared with the radiation from the black paint on the surface of 
the radiation box. This was possible on this night, as there was no wind, and 
radiation was fairly constant. 

In my first experiments with black and white cloths, they were found to be 
cooled to an unequal amount ; but as the cloths used on this occasion were 
what first came to hand, and happened to be of unequal thickness and texture, 
and as there was wind blowing at the time, the heating effect of the passing 
air acted unequally on the different cloths, and prevented them from being cooled 
to the same amount ; hence the necessity of using cloths of equal texture in 
experiments of the kind, especially when wind is blowing. 

It will be observed that these experiments do not show any difference in 
the radiating powers of white and black cloths ; nor do they show any differ- 
ence in the radiating powers of cotton, wool, and paint. All radiate equally well, 



38 



MR JOHN AITKEN ON DEW. 



and have their surfaces cooled to the same amount when exposed to the same 
radiation. It will be noticed that the temperature of the radiating surfaces 
varied during the experiments, and was from 6 to 8 degrees below the 
temperature of the air. 

These experiments make no claim to any great degree of accuracy ; the 
conditions under which they are made make it difficult to get correct results, 
as the readings have to be taken with the aid of a lantern in the open air on 
cold nights, and as special thermometers had not been prepared for the radia- 
tion boxes, the thermometers used had to be partly withdrawn from the boxes 
before reading; there may therefore be a slight inaccuracy in the temperatures 
given. The error from this cause is not likely to be more than a quarter of a 
degree, and if there had been any great difference in the radiating powers 
of the surfaces, it would have shown on a scale of 6 to 8 degrees. 

The following table gives the result of a comparison made between the 
radiating powers of grass and garden soil, on a calm evening when the air was 
dry. One of the thermometer boxes was sprinkled over with the soil, and over 
the other was put a layer of cut grass just sufficient to conceal all the black 
surface, and pressed down so as to make as flat a surface as possible : — 



Temperature of air. 


Temperature of grass. 


Temperature of soil. 


34° 


25°-5 


25° 


35° 


27° 


26°-5 


35° 


27° 


26° 


35° 


27° 


26°'5 


35° 


27° 


26°5 



From the above it will be seen that the garden soil was colder than the 
grass on this evening. When the grass was removed from the box and the soil 
compared with the black paint on the other box, the soil was found to 
be a little colder than the black paint, but not so much as it was colder than 
the grass. The reason for the soil being colder than the black paint would 
appear to be due to the evaporation taking place from its surface; the dew- 
point at the time was very low, and the top of the soil showed signs of 
drying. Compared with grass, this was not the reason for the difference, as 
the grass was slightly damp. The higher temperature of the grass would rather 
appear to be due to the nature of its surface. The passing air would communi- 
cate more heat to its irregular surface than it would to the more even one of 
the soil. Grass and soil were compared on other evenings on which the air was 
not so dry, and the exposed surfaces had vapour condensed on them; on 
these occasions the two surfaces radiated almost equally well. 

This comparison of the radiating powers of grass and soil gives no support 



MR JOHN AITKEN ON DEW. 



39 



to the idea that the greater wetness of grass on dewy nights is owing to its 
greater radiating power. The radiating powers of the two surfaces seem to be 
practically the same; and if neither grass nor soil received heat from the ground, 
the soil would cool lowest, because the grass in its natural condition would get 
more heat from the passing air, on account of its surface being irregular and in 
small pieces, as we know that small surfaces receive from this cause much more 
heat, per unit of area, than larger ones, this being particularly the case when 
there is wind. From which we see that the smallness of the blades in grass is 
really an advantage, and prevents their surfaces being cooled by radiation so 
much as they would be if they were larger. 

The number of substances tested for their radiating powers at night is not 
so great as was hoped for, on account of the rare occurrence of evenings on 
which work of this kind can be done in this climate; for not only must the sky 
be free from passing clouds, in order that the amount of radiation may be as 
constant as possible, but the air must also be very dry, in order that the dew- 
point may be lower than the temperature of the cold radiating surfaces. 
If vapour gets condensed on the radiating surfaces, the radiation from the film 
of ice, or water, will interfere with the results. In making the experiments, 
a large sheet of glass was generally exposed alongside of the radiation boxes, to 
show if vapour was being deposited on the radiating surfaces. But even with 
this precaution we cannot be sure we are testing the radiating powers of some 
substances experimented on, because some kinds of matter have an affinity for 
water, and condense vapour on their surfaces from unsaturated air. As an 
example of uncertain results, I may mention a comparison made between salt and 
sugar. These two substances have been found by other observers to radiate 
very unequally at 100° C. — sugar radiating twice as much as salt. When tested 
at night, they were found to radiate equally well; but as both substances have 
an affinity for water, their surfaces would have a film of moisture over them, 
which would increase the radiating power of the salt, and thus make the test 
of no value. 

Among the few substances that have been found to radiate less heat at 
night than a black surface is sulphur. On the night of the 7th December, when 
the air was very dry and the glass plate kept undewed, the following read- 
ings were taken : — 



Temperature of air. 


Temperature of black surface. 


Sulphur. 


27° 
26° 


21° 
19° 


23° 
21°-25 



The sulphur was sifted over the one thermometer box and the other left bare. 



40 



MR JOHN AITKEN ON DEW. 



It will be observed that the black surface radiated one half more than the 
sulphur. This experiment suggests that a sprinkling of sulphur might be used 
as a protection to delicate plants on frosty nights, but whether it would pay or 
not experience alone can determine. 

Polished tin was also tested, a sheet of tin being placed over one box, and 
another sheet painted black put over the other, so as to make the conditions of 
both boxes similar. The amount radiated by the tin was small; when the 
temperature of the black surface fell 7°, the tin only fell about 1°, more or less, 
according to the perfection of the polish of its surface. 

For meteorological purposes the following observations made on the radiat- 
ing power of snow will be useful. I regret that owing to the absence of snow 
so far this winter, I have only had one opportunity of making observations on 
this substance. In the following table will be found the readings given by the 
thermometer boxes, one of which was left bare, and gave the radiation of black 
paint, while over the other was put a thin layer of snow. This was done on 
the forenoon of the 10th December, and readings were begun shortly after 
mid-day, and taken from time to time till evening: — 



Hour. 


Air. 


Black. 


Snow. 


Difference. 


12-30 p.m. 


28° 


24° 


21° 


-3° 


1 


28° 


24°-5 


22° 


-2°-5 


2 


26°-8 


22° 


20° 


-2° 


5 


23° 


15°-5 


16° 


+ 0°-5 


5-30 „ 


21° 


15° 


15°-5 


+ 0°-5 


6-30 „ 


21° 


13° 


13°-5 


+ 0°-5 


8 


19° 


9° 


.10° 


+ 1° 



In the above table, the first column gives the hour at which the temperatures 
were taken. In the second column are the temperatures of the air; in the 
third are the temperatures of the black radiating surface; in the fourth are 
the temperatures of snow surface; and in the fifth column are the differences 
between the temperature of the snow and the black surface at the hour the 
readings were taken. The day on which this comparison was made was fine, 
clear, calm, and frosty, with the sun shining brightly. The radiating surfaces 
had a clear view of the sky, but were protected from the direct rays of the 
sun. 

It will be observed that while the sun was high the snow surface was very 
much colder than the other; while the black surface only fell 4° below "he 
temperature of the air, the snow fell 7°. As the day advanced, and the sun 
sunk towards the horizon, this difference decreased to 2°*5 at 1 o'clock and to 
T at 2 o'clock; and at 5 o'clock, by which time the sun had set, the snow 



ME JOHN AITKEN ON DEW. 41 

was a little warmer than the black surface, a condition in which it remained 
during the evening. 

The reason for the snow being colder than the black surface during the day 
would seem to be, that both surfaces radiate and absorb " dark heat " about 
equally well, both surfaces therefore throw off about the same amount of heat; 
but while this is the case, their absorbing powers for the heat of the sun are 
very different, and though the sun was not shining directly on the surfaces, 
yet there is a considerable amount of its heat reflected to the surface of the 
earth from the atmosphere overhead. Now a black surface absorbs most of 
this reflected heat that falls upon it, while the snow absorbs very little. Hence, 
while both surfaces are radiating about the same amount of heat, the black 
surface is absorbing far more than the snow, and thus keeps warmer. As 
the sun sinks, the amount of its heat reflected by our atmosphere gets less and 
less, and the difference in the temperature on the two surfaces diminishes; and 
when at last the sun is quite under the horizon the temperature of the two 
surfaces becomes nearly equal. It will be, however, observed, that they never 
become quite the same, the snow being generally about half a degree warmer 
than the other. The whole of this difference is not, however, owing to differ- 
ence in radiating powers ; the snow will tend to give a slightly higher reading 
on account of its surface being rougher than that of the paint, thus causing it 
to receive more heat from the passing air than the black surface. And, further, 
from the conditions of the experiments, the readings being taken during a 
falling temperature, and the snow not being a good conductor of heat, the 
thermometer under it will take longer to fall than the one under the blackened 
metal. From these conditions it seems probable that there is not much differ- 
ence between the radiating and absorbing powers of snow and black paint at 
night, while the difference is very considerable during the day. 

It has been suggested to me that this difference in the radiating and 
absorbing powers of snow and black surface, such as soil, &c, will enable us to 
explain a difficulty long felt, regarding the hour at which the diurnal variation 
of temperature begins in countries covered with snow. Over those parts of the 
surface of our globe, where there is no snow, the temperature of the air begins 
to rise before sunrise, whereas in snow- clad regions this change does not take 
place till the sun is above the horizon — the explanation would appear to be 
that where the surface of the ground is dark it absorbs the heat of the sun, 
and warms the air whenever the rays begin to shine into the air overhead; 
but where covered with snow it is but little warmed by these early reflected 
rays, and it is not till the sun gets higher and shines on the surface of the 
earth that its effects begin to be felt. 



VOL. XXXIII. PART I. 



42 MR JOHN AITKEN ON DEW. 

General Remarks. 

We see as a result of these experiments, that in our climate at least, water 
vapour is almost constantly rising from the ground, and this takes place from 
fallow land, from grass land, and from roads, even on nights on which there is 
heavy dew. There seems to be but little doubt that the tide of vapour almost 
always flows outwards from the earth, and ebbs but rarely, save after it has 
been condensed to cloud and rain. The question as to whether any surface is 
in a condition to lose or gain moisture on a dewy night depends on its more 
or less perfect heat communication with the earth. Those surfaces, such as 
soil, rock, stones &c, which are in good heat communication with the earth, 
tend to keep warm, and to lose moisture ; while those surfaces not in good 
communication with the earth, such as leaves of plants, roofs of sheds, &c, 
tend to lose their heat, and gain moisture. This is the reason why grass 
tends to collect true dew, while stones on the ground remain dry. Grass is a 
bad conductor, and forms a non-conducting layer over the ground, preventing the 
earth from losing its heat. The inside of this covering is hot by contact with 
the earth, while its outside is cooled by radiation; and as the grass is a bad 
conductor, its exposed surface gets cooled by radiation to a lower temperature 
than the better conducting soil and stones ; hence the appearance of dew on it, 
while the earth is dry. 

Since vapour is constantly rising from the earth on dewy nights, it follows 
that any measurements of dew we may make ought not to be added to the 
rainfall, as the water so collected is in no sense a measure of the moisture 
returned to the earth at night, nor is it even a proof that any water is then 
returned. The amount of dew measured is simply a somewhat rough indication 
of the amount of moisture received by plants and other bodies not in heat com- 
munication with the ground ; while the ground itself does not receive any, but 
is rather giving off vapour. 

Dew is most copious during clear weather, and these experiments show us 
that this condition of weather has a threefold action in the production of dew 
— first, cloudless skies are necessary at night, in order that radiation may be 
strong, and the surfaces of bodies cooled low enough to condense the vapour; 
second, clear skies are necessary in order that a' copious evaporation may take 
place under a hot sun during the clay ; and third, the same conditions are 
necessary that the ground may be highly heated by the sun, and a large amount 
of heat stored up during the day to be spent in evaporating an abundant 
supply of vapour during the night. 

What are known as radiation fogs arc generally supposed to be due to cold 
air flowing down, at evening, from higher levels to lower and warmer ones 
and the mixing of the airs resulting in a foggy condensation. The more 



MR JOHN AITKEN ON DEW. 43 

probable explanation now seems to me to be, that they are caused by the 
uprising of the hot air and moisture from the ground, mixing with the colder 
air above the grass, much in the same way as a fog is produced over a river in 
sunny weather when the water is warm. So far as my observations go, these 
fogs generally form over flat damp fields, after hot sunny clays, and they have 
been seen where there was no high ground from which cold air could flow in. 

There almost seems reason for supposing that much of the moisture 
collected on grass, and which looks like true dew, may under many conditions 
be fine rain from fog formed in the manner above described. Because the hot 
air and vapour rising through the grass will tend to form fog, where it mixes 
with the cold air near the upper part of the grass, and if there is little wind 
this fog will settle on the blades. Under most conditions this fog will not 
form above the grass, and will not therefore be visible. It will often not form 
above the blades, because the hot moist air may there meet with too much dry 
air to supersaturate it, but there seems reason for supposing that it will be 
often formed amongst the stems of the grass. 

During frosts we have excellent opportunities for studying the condensation 
of the vapour of our atmosphere, because it remains in the position where it is 
condensed and is easily seen, being neither absorbed by the ground nor dropped 
from the plants, &c, on which it may be deposited. I took the opportunity 
afforded by two nights of this kind for observing two opposite conditions of 
the air, and I shall here describe the effects of the radiation on the nights of 
the 14th and 15th November. During the afternoon the canopy of clouds that 
had hung over the earth for some days was gradually drawn aside, and moved 
away southwards. By 5 p.m. on the 14th the sky was cloudless. There was 
only a very slight movement of the air from the north, the radiation was strong, 
and the air dry. These conditions continued all night, and the minimum 
thermometer in the screen fell to 25°. 

Next morning the ground and the grass were frozen. It was what is called 
a black frost. There was no hoar-frost on the trees, and what little there was 
on the grass was irregularly distributed. All the little hollows, of about a foot 
square in area and under, had a deposit of hoar-frost, while the higher parts of 
the grass had none. As there was no wind, and only a slow movement of the air, 
this peculiar distribution would not be caused by the heating effect of the passing- 
air on the higher and more exposed blades, but was probably owing to its 
dryness. The small hollows being less freely exposed to the circulation, the 
air in them became more moistened from the vapour rising out of the ground 
than the air a little higher up, where it got mixed with a larger amount of the 
dry air. The test surface on the ground was quite dry at 9 p.m., and also next 
morning, showing that the ground had been giving off vapour all night. 

In contrast with this, let us now look at the condition of matters on the 



44 MR JOHN AITKEN ON DEW. 

following morning. During the whole of the 15th the air remained calm and 
frosty, and the cold intensified during the night. On the morning of the 16th 
the minimum thermometer indicated a temperature of 19°. On this occasion 
we had a hoar or white frost. Grass, fences, shrubs &c, were all white, and 
the trees even to their top branches. The air on this occasion had evidently got 
cooled to near its dew-point, and moisture had condensed on almost every ex- 
posed surface, causing nature to present a remarkable contrast to its appearance 
on the previous morning, though both mornings were frosty. 

We shall now refer in more detail to some of the points most worth 
noticing on these mornings. It was observed that the distribution of the hoar- 
frost on the grass on the morning of the 16th was the reverse of what it was 
the previous morning, the high blades on this occasion having rather a thicker 
coating of hoar-frost than those lower down. The reason for this was that 
the higher blades were exposed to the passing air, which on this occasion was 
saturated; whereas those on the hollows had to depend for their supply on 
what rose from the ground, which could not be much under the conditions, as 
the bottom of the grass and the top of the soil were cooled below the freezing- 
point, and most of the rising vapour would be trapped before it reached the 
surface. We may also note here that the test surfaces on the soil were quite 
dry, and that the slate and iron weight resting on the grass were free from 
deposit ; while the elevated slate and weight, the grass, and almost everything 
else had a coat of hoar-frost, showing that the ground kept hot enough to give 
off moisture. An examination of the bare soil also showed that at most parts 
of its surface vapour was being given off. Wherever the contact with the 
ground underneath was good, no hoar-frost formed, and it was deposited only 
on the small clods that were lying on the surface; of course, there was plenty 
of hoar-frost on the under sides of the large clods, but none on their upper 
surfaces. 

The slates and weights resting on the grass were frequently examined while 
the frost lasted, which it did till the morning of the 19th. During all this time 
the radiation was great, and the temperature very low. The minimum on 
different nights was as low as 12 0, 5, 17°5, and 19°. During all that time, though 
the ground received no heat direct from the sun, and but little in any way 
from above, yet the supply from beneath was sufficient to keep the tempera- 
ture of the surface above the dew-point, and the slate and weight in contact 
with the ground remained black amidst the surrounding whiteness. 

Another peculiarity of mornings such as this — which arc of frequent occur- 
rence during winter — is the deposition of moisture on trees. During my observa- 
tions in summer I never saw shrubs dewed to a height of more than a few feet 
from the ground, while in winter tall trees frequently have vapour deposited on 
them to the top branches. But as my observations in warm weather are very 



MR JOHN AITKEN ON DEW. 



45 



limited on this point, and owing to a simple wetting not being so conspicuous 
as hoar-frost, it is possible trees may occasionally get wet in summer with clew 
without its being observed. It however seems probable that it will be of much 
more frequent occurrence in winter than in summer, owing to the much longer 
absence of the sun during winter nights. 



Radiation from Snow."" 

In a previous part of this paper reference has been made to the radiating 
and absorbing powers of snow. In the experiment detailed, comparative 
readings are given of the temperature of snow and of a black surface exposed 
in shade on a bright day. The temperatures taken under the conditions then 
existing showed the snow to be much colder than the black surface. This 
conclusion has since been confirmed by a number of readings with the radia- 
tion thermometer under different conditions of climate. Of these observations 
it will only be necessary to give those taken on two days. The following 
temperatures were taken on the 19th January. In these tables the contents 
of the columns are arranged as in previous one. 



Hour. 


Air. 


Black. 


Snow. 


Difference. 


10.0 A.M. 
2.0 P.M. 

2.30 „ 
3.30 „ 


20°-2 
30°-0 
30°1 
30°-2 


16°-2 
30°-0 
30°-2 
30°-2 


12°-0 
26°-0 
26°-4 
28°-0 


-4°-2 
-4°-0 
-3°-8 
— 2°-2 



In the morning the sky was clear, but by 2 p.m. it became overcast, with a 
thin uniform covering of clouds ; and at 3.30, it was beginning to snow. The 
next readings were taken on the 5th February. 



Hour. 


Air. 


Black. 


Snow. 


Difference. 


10.0 A.M. 


23°-0 


28°-8 


25°-0 


-3°-8 


12.0 P.M. 


25°-5 


31°-1 


26°-l 


-5°-0 


2.0 „ 


30°-0 


34°-8 


30°-0 


-4°-8 


3.30 „ 


31°-0 


34°-5 


30°-5 


-4°-0 


5.15 „ 


31°-5 


29°-0 


29°-0 


-o°-o 



On this occasion also the sky was overcast. In these two tables exactly 
the same result is recorded, the black on both occasions being again much 
warmer than the snow. These two tables are given, as they were taken under 
quite different conditions. When the temperatures given in the first table 

*Read March 1, 1886. 



4(5 MR JOHN AITKEN ON DEW. 

were taken, the air was warmer than the radiating surfaces, while in the 
second the air was colder than the exposed surfaces, except towards evening. 
A number of other readings were taken under different conditions, but with the 
same results ; the snow was always colder than the blacker surface during day, 
while other observations made at night show their radiating powers are then very 
similar. 

Part of the cooling produced by the snow surface shown in the above tables 
would be due to evaporation from the snow. The amount due to this cause 
was not great, as the difference between the wet and dry bulb thermometers 
was small at the time. I regret, however, that the readings of these instruments 
have been lost, so I write from memory, It will, however, be observed that the 
difference in the radiating powers of the two surfaces continued during the 
whole time the readings were taken on the 19th January, though the weather 
changed to snow, and the air at that time would be nearly saturated. The 
readings given in the tables therefore give the total cooling effect of the snow, 
which is produced by two causes — radiation and evaporation. 

This small absorbing power of snow for heat, reflected and radiated from 
the sky during the day, must have a most important effect on the atmosphere, 
causing its temperature to be much lower when the ground is covered with snow 
than when free from it. So that when a country becomes covered with snow 
— other things being equal — it will be accompanied by a depression of the 
mean temperature of the air ; and, further, as cold tends to produce a stable 
condition of the atmosphere, not creating the current disturbances of heating, 
it would appear that once a country has become covered with snow there will 
be a tendency towards glacial conditions. 

But this poor absorbing power of snow is not the only way in which it 
tends to produce a glacial climate. Snow, in addition to being a bad absorber 
of the heat of the sky, is also a very poor conductor of heat. In illustration of 
this, let me mention a few temperature observations made while the ground 
was covered with snow during January last. On the 18th of that month 
there was about b\ inches (140 mm.) of snow on the ground; the night was 
clear, and radiation strong. At 8 p.m. the temperature of the surface of the 
snow was 3°, and a minimum thermometer also on the snow showed that it had 
been at 0° at an earlier hour. Taking a maximum thermometer, the index 
was brought down below the freezing-point, and the bulb plunged through the 
snow down to the grass. On examining it a short time afterwards the index 
was at 32°. In confirmation of this reading, it may be mentioned that on 
removing the snow the top of the soil was found to be unfrozen. These 
observations showed that there was a difference of about 30° between the 
temperature of the top and the bottom of the snow — that is, a distance of 
•)}, inches. 



MR JOHN AITKEN ON DEW. 47 

During the night the temperature of the air fell 5 degrees lower, so that the 
surface of the snow would be kept about zero for most of the night, yet next 
morning at 9.45 the bottom of the snow was still at 32°. The temperature of the 
surface of the snow had risen at this hour only to 8°*5. These observations 
were repeated on other occasions when the coating of snow was thinner ; there 
was then less reduction in the temperature of the surface, but on all occasions 
when the snow was a few inches deep, the surface of the soil remained at 
32°. As the ground was frozen when the snow fell, it would appear that the 
earth's heat slowly thawed it under the protection of the snow, and the 
temperature of 32°, which was below the surface when the soil was frozen, 
gradually rose to it, where it of course stopped, and the rising heat was spent 
in melting the snow. 

The protection afforded by the bad conducting power of snow is evidenced 
in our climate, by the amount of vegetation that takes place underneath it, on 
those occasions when we have had snow on the ground for a length of time. 
After the snow is gone, many plants are found to have grown, and some 
advanced nearly to bloom under its protection. This same influence may, 
however, be seen at work in a more marked manner in spring on the slopes of 
the Alps and other lands covered with snow all winter. As the snow recedes, 
and the surface of the earth is gradually laid bare, the vegetation is found to be 
in an advanced state — many of the flowers, if not in bloom, are just ready to 
open. 

This bad conducting power of snow, compared with soil and rock, will 
evidently tend to lower the temperature of the air over snow-clad lands, as a 
few inches of snow in our climate conserves the earth's heat, and prevents its 
surface being cooled below 32°. The surface of the snow thus gets very much 
colder than the bare surface of the earth would have been if no snow had been 
on it, and the air is thus cooled much more over a snow surface than over one 
of bare earth. 

To get evidence of the statement that the surface of a country covered 
with snow is much colder than it would have been if free from snow, we have 
only to examine the surface of the ground under the two conditions. The 
surface of snow covering the ground receives so little heat from the earth 
that it gets cooled by radiation to such an amount that it is almost always 
during frost cooled below the dew-point, and is covered with a heavy deposit 
of hoar-frost. During the late snow I have frequently noticed a thickness of 
more than 12 mm. of beautiful ice crystals of this kind deposited on its surface. 
But while the snow is cooled so much, and has this deposit on it, the surface 
of the soil where it has been laid bare keeps quite free from this deposit, as it 
receives sufficient heat from below to keep its temperature above the dew-point. 
The air over snow-clad lands is thus always in contact with a highly-cooled 



48 MR JOHN AITKEN ON DEW. 

surface ; whereas when there is no snow, the air rests on a warmer 
one. 

Taking then these two things together, the bad absorbing power of snow 
and its small conducting power for heat, we see that when snow has once got 
possession of a land, the tendency to glacial conditions is greatly increased ; 
and if it were not for the disturbing effects of heat in warmer climates, 
it is hard to say how far glacial conditions might spread towards the 
equator. 

Up to the time when the previous part of this paper was given in* I had 
been unableto find records of any meteorolgical station at which the condition 
of the ground with regard to snow had been recorded in addition to the usual 
temperature observations ; even yet I have not succeeded in getting suitable 
records for our climate, and one cannot help regretting that observations of 
this kind are not more frequently kept in this country. 

My conclusions, however, with regard to the effect of snow on climate, I 
now find are confirmed by the observations of Dr Woeikof, an abstract of 
whose work in this direction has just appeared in Nature of 18th February 1886 
(vol. xxxiii. p. 379). Dr Woeikof has approached the subject from the observa- 
tional side, and as his results bear directly on ours, I shall quote the following- 
paragraph from the abstract referred to : — 

"The year 1877 was a striking instance of how the absence of snow was 
accompanied by a far less notable lowering of temperature during the preval- 
ence of anticyclones, than would have been the case had the soil been covered 
with snow. In 1877 there was no snow in Eastern Russia until Christmas, and 
in November and December the anticyclones occurred, accompanied by no 
wind, or only by feeble breezes. Quite bright weather lasted in December for 
more than ten days ; and still, in the region which remained uncovered with 
snow, no great cold was experienced, as usually happens in such circum- 
stances; the minima were 8° to 9° above their average values. The same 
conditions were noticed during the winters of 1879-80 and 1881-82 in West 
Europe, as shown by Dr Billwiller in the Zeitschrift fur Meteorologie for 
1882." 

In the next paragraph, the abstract states that, in the opinion of Dr 
Woeikof, the higher temperature of November, as compared with March in 
South-East Russia, is due to the ground not being usually covered with snow 
in November. 

These observations of Dr Woeikof confirm the conclusions arrived at in this 
paper from a consideration of the properties of snow. In the opinion of Dr 
Woeikof, the low temperature accompanying the snow is to be attributed 
to its bad conducting power. While we quite agree with the observer 

* Note added 26th February 188G. 



MR JOHN AITKEN ON DEW. 49 

that the bad conducting power of snow will be a cause of tlie lower tempera- 
ture, yet we think that the observations recorded in this paper show that 
radiation plays a most important part in producing this result. It has been 
long well known that snow receives less heat from the direct rays of the sun 
than the surface of a dark body like soil or rock, and we now also know that, 
under any condition of sky yet tested, it absorbs but little of the sky radiation. 
From this we see that as the surface of the snow, under all conditions of 
sky, receives less radiant heat from without than the surface of the ground, 
the air in contact with it will be more cooled than the air over bare soil or 
rock. 

In the radiation temperatures above recorded, the snow was generally 
about 4 degrees colder than the black surface during the day. We must not 
from this suppose that these 4 degrees are the greatest difference that could 
exist in the radiation temperatures of the two surfaces. These 4 degrees 
simply represent the difference that was maintained under the conditions when 
the tests were made. If the air circulation had been greater, the difference 
would have been less, and both would have been nearer the temperature of the 
air ; and if the circulation had been less, the difference would have been 
greater. But while there may be a variation in the difference of the tempera- 
tures of the two surfaces, there will be but little difference in their respective 
cooling effects, as with a quick circulation a large amount of air will be cooled 
a little, while, when the circulation is slow, a little air will be cooled a great 
deal. Not only so, but on account of the temperature of space being so much 
colderthan the surface of the snow, the temperature of the snow will tend to sink 
about the same amount below the temperature of the air, even though the air be 
greatly cooled ; so that, under the same conditions of radiation and atmospheric 
circulation, however much the air may have been cooled, the two surfaces will 
tend to maintain the same difference in temperature, and the snow will always 
tend to cool the air more than a black surface, when the surfaces are colder 
than the air, or to heat it less when the surfaces are warmer. 

It is therefore evident that this radiation effect will be one of the causes 
tending to produce the lower temperature of the air while snow is on the 
ground, and it seems probable that the snow will not only reduce the minima 
temperatures, but also the maxima. It seems also probable that the bad 
absorbing power of snow will have a most important influence in retarding the 
approach of warm weather, as the earth under snow receives far less heat from 
the sun with the approach of spring than if the ground had been free from 
snow. This is, of course, altogether apart from the question of the retardation 
of the approach of warm weather by the sun's heat being spent in melting the 
snow, instead of warming the air. 

VOL. XXXIII. PART I. G 



50 MR JOHN AITKEN ON DEW. 

Summary. 

Our principal conclusions may be summed up as follows : — First, From the 
experiments made with (a) the inverted trays, (b) by weighing small areas of 
turf, and (c) by observations of the temperatures on and under the grass 
during dewy nights, we have concluded that vapour is almost constantly rising 
from grass land, by night as well as day, in our climate. Second, From experi- 
ments made with (a) inverted trays, (b) by weighings of small areas of soil, and 
(c) by observations made with small test condensing surfaces, on dewy nights, 
we have concluded that, under most conditions of our climate, vapour rises 
from uncultivated areas of soil during night as well as clay. It follows from 
these two conclusions that dew never " falls " on the earth : and for reasons 
given, it is only deposited on plants, and other bodies, not in good heat com- 
munication with the ground. Third, That the greater part of the dew condensed 
on bodies near the ground is formed of the vapour rising at the time from the 
earth, and very little of it from the vapour that rose during the day. Fourth, 
That dew forms copiously on roads, but owing to the stones being good con- 
ductors of heat, the vapour is deposited on the under sides of the stones, and 
not on the top as on grass. Fifth, Wind hinders the formation of clew by 
preventing an accumulation of clamp air near the ground. Sixth, The " dew- 
drop " formed on grass and other plants is not dew at all, but is formed of the 
exuded sap of the plant. Seventh, Almost all substances, such as black and 
white cloths, garden mould and grass, radiate equally well at night. Among the 
few exceptions observed are polished metals and sulphur. Eighth, A covering 
of snow on the ground lowers the mean temperature of the air. 

FURTHER REMARKS ON DEW. 

Appendix. 

(Read 19th July 1886.) 

Since the preceding paper was written, a few opportunities have occurred 
for continuing the investigation under different conditions of climate, and some 
additions have also been made to strengthen the exudation theory of the " dew- 
drop " on grass and other plants, of which I shall here give a short account. 

At the beginning of the paper, evidence is adduced to show that water 
vapour is almost constantly rising from the ground during night, as well as day, 
and it is there noted that the experiments were somewhat unsatisfactory on 
account of the rather damp condition of the soil at the time, the dry season 
being over before the investigation was made. In order to supplement these 
observations, a few others were made in the beginning of July of this year, when 
the soil was in about as dry a condition as it almost ever is in this climate. 



MR JOHN AJTKEN ON DEW. 51 

• 

An inverted tray was placed over bare soil which was so dry and powdery 
that it rose in dust when the edge of the tray was pressed into it. The tray 
was not placed on the ground till after 9 p.m. — that is, after the soil had lost a 
good deal of heat and moisture — yet in two hours the inside was wet, and in 
the morning it was covered with drops. While this experiment was going on, 
another tray was placed on the lawn at a place where the grass was burnt quite 
brown. The inside of this tray was also wetted, and to about the same amount 
as the one over the bare soil. It may be noted here, that the positions for 
making these tests were selected on account of their extreme dryness. The 
bare soil was light and open, while the lawn was extremely dry, having been 
laid down a few years ago with every precaution to ensure this condition ; the 
under soil is dry and sandy, it was moreover well drained, the upper soil was 
removed, and a good depth of ashes put in its place, then a layer of sand, on 
which was put the turf with its inch or two of soil. A drier position could 
scarcely have been selected for the trial, and yet the result showed that in our 
climate bare soil and grass land, even when very dry, continue to give off vapour 
during dewy nights. 

A few experiments were also made on this subject in March last at Hyeres, 
in the south of France. In order that the test might be as severe as possible, 
I selected a spot where the soil seemed driest and most exposed to the sun and 
the wind; and as the soil was stony and lying on the hill-side, it could 
have no supply of water from below. An inverted tray placed over this arid 
ground collected a surprisingly great amount of moisture. The following are 
the notes of one of the tests made at Hyeres on the 27th March last :— At 5.15 
p.m. the sun had ceased to shine on the place selected for the experiment ; at 
that hour the temperature of the soil was 73° F. at 3 inches below the surface, 
and 59° at 12 inches. At 5.45 the tray was put on the ground. Examined at 
7.15 p.m. the outside was dry, but inside was quite wet, and by 10 p.m. the drops 
were so large they ran down the inside when the tray was placed vertically. 
This great amount of wetting was probably due, not only to the ground being 
highly heated during the day, but also to a considerable fall in temperature at 
night, by the cooling produced under the clear skies of that climate. 

I much regret I have been unable to get any trustworthy information 
regarding the movement of the vapour near the surface of the ground in barren 
and desert countries. I have, however, received some information from 
travellers who have been in Australia and parts of South Africa, where rain 
does not fall for months at a time, and it goes to prove that even in these dry 
countries vapour rises from the ground at night, as they often found the under 
side of their waterproof bedding placed on the ground to be wet after camping 
out at night. One would scarcely have expected much moisture to be collected 
in this way on account of the warmth of the sleeper's body keeping up 



52 MR JOHN AITKEN ON DEW. 

the temperature of the condensing surface. It therefore seems probable 
that the moisture will collect under those parts of the waterproof which are 
beyond the influence of the sleeper's body. 

While the experiments above referred to on bare soil and grass land were 
being made on ground exceptionally dry in July, those with slates placed on 
the road were repeated. As in the experiments described in the first part of 
this paper, the slates placed on the hard dry part of the road and on the 
gravel got quite wet on their under sides at night, thus showing that, even 
under the exceptionally dry conditions existing at the time, vapour was still 
rising at night from the hard and arid roads. 

In connection with the action of stones lying near the surface of the ground, 
we may here refer to a result observed by agriculturists, on which it seems to 
throw some light. It has been remarked that the removal of small stones from 
fields where the soil is light and open, often has a prejudicial effect on the 
crops. -It must be admitted that accurate information on this point is not 
easily obtained, but the impression in some parts of the country certainly is, 
that the removal of small stones from fields is not to be recommended. Now 
the removal of stones may act prejudicially in different ways. In some cases 
the disintegration of the stones may add to the richness of the soil ; their 
removal may therefore in some cases decrease the natural fertility of the field. 
No doubt the removal of the stones will permit of a more rapid evaporation from 
the soil during the day, but it does also seem probable that the peculiar action 
of stones, in trapping the moisture before it comes to the surface at night, will 
have a beneficial effect on light and dry soils. Part of the moisture is trapped 
by them before it can escape from the surface at night ; and when the sun 
rises, the stones becoming warmer than the soil under them, the moisture 
leaves the stones and condenses in the soil underneath. In this way stones 
would seem to have a sort of conserving action on the moisture, and tend to 
check the prejudicial effects of continued dry weather. 

In confirmation of this conserving action of bodies lying on the surface of 
the ground and improving its fertility, I would refer to a letter in Nature, 
vol. xxxiii. p. 583, by Lieut. -Col. A. T. Fraser. As this letter is so 
interesting, and bears directly on our subject, I may be allowed to quote 
from it here. At the beginning of his letter he says : — " Having had occasion 
to lay out a large quantity of iron hoes and picks, without handles, on the hard 
ground of an open inclosure in one of the driest districts of India (Bellary), 
where, in fact, these implements had been collected in the face of a scarcity, it 
was found, after they had lain a couple of months, that a thick, weedy, but 
luxuriant vegetation had sprung up, enough, though there was no rain, to 
almost hide the tools." 

Lieut.-Col. Fraser also says he had previously noticed in the tropics a 



MR JOHN AITKEN ON DEW. 53 

similar stimulating effect produced on vegetation when tools were left lying on 
the surface, but was unable to account for it till he read the abstract of the 
first part of this paper, when he at once recognised the manner in which the 
tools lying on the surface acted in hot and dry climates by checking the 
escape of vapour at night. No doubt much of the increased fertility observed 
would be due to the wetting the plants received by the vapour condensed on 
the under sides of the tools ; still it will be admitted something must also be 
owing to the reduced evaporation during the day, produced by the metal tools 
checking the escape of the vapour. 

This conservation of moisture by stones and other bodies lying on the 
surface of the ground, and its up and down movement during night and day, 
may be easily seen in the experiment with the slates. Examined at night the 
road under the slates is as dry as the exposed parts, while the under sides of 
the slates are wet ; but if examined at a certain time in the morning, the under 
sides of the slates will be found to be dry, while the road under them is wet. 
But, if the slates are not examined till a later hour, both the slates and the 
road under them will be found to be dry, the moisture being driven deeper and 
condensed among the stones lower down. 

Many people, after reading the conclusions arrived at in the first part of this 
paper, seem to have a difficulty in accepting the theory that vapour is con- 
stantly rising from the ground during night as well as day, and that the dew 
on grass is formed of this rising vapour, because it seems to them to contradict 
the teaching of Dr Wells, and it also appears to be at variance with their 
experience. A little consideration will show that the results established by 
Dr Wells are in no way affected by it. That investigator certainly did 
not think that much vapour rose from the ground at night, yet he was well 
aware that some might rise ; his investigation was however principally con- 
fined to the condensation of the vapour after it is in the air, and he gave 
comparatively little attention to its source ; whereas in this investigation 
Wells' results are accepted with regard to the condensation, and an attempt is 
made to extend the subject by investigating some parts not worked out by him. 

Others again have made a difficulty to the acceptance of this theory by 
extending the conclusions arrived at in this paper to other conditions than those 
for which they are true. They have assumed that if dew on grass and on bodies 
near the ground is formed of vapour rising at the time, then the dew found on 
bodies higher up in the air must also be formed of vapour rising at the time 
from the ground immediately underneath ; and as this conclusion is opposed to 
experience, they seem inclined to dismiss the whole theory as unworthy of 
consideration. When we come to investigate what is taking place in nature 
we will see that this extension of the conclusion is by no means justified. 

The reason why it is concluded that the dew on the grass, and on bodies 



54 MR JOHN AITKEN ON DEW. 

close to the ground, is formed of vapour rising from the ground, is that at 
night the ground under the grass is always in a condition to give off vapour, 
and this rising vapour will tend to displace that which rose during the day ; 
the stems and blades of grass will thus become surrounded by vapour that 
has risen during the night. A further reason is, that the ground under the 
grass is much warmer than the air over it, and the air in contact with the 
moist earth is nearly saturated ; the tension of the vapour in the air rising 
through the stems of grass is thus higher than that in the air over them, and it 
is therefore in a more favourable condition for condensing and forming dew 
than the air higher up. This hot rising vapour will often indeed yield dew 
when the air over the grass can give none. 

When, however, we come to consider what takes place higher up above the 
grass, or even at the tops of the blades, we meet with a much more compli- 
cated condition of matters, and we are now able to say very little about the 
source -of the vapour condensed at these higher positions. Whenever we get 
above the protection of the grass, into the parts of the atmosphere exposed to 
air-currents, we can say very little as to the source of the vapour existing there, 
either as to the place where it changed to vapour, or the time when this 
change took place. No doubt some of the molecules in this upper air will 
have risen but recently from the ground, but some of them will certainly — if 
there is the slightest wind — be molecules that have risen during the day, and 
no doubt some of them will have ascended into the air many clays previously ; 
and while some will have but recently come from the ground immediately under- 
neath, others will have travelled from lands and oceans far away. But while 
this may be so, it in no way affects the conclusion that vapour is almost con- 
stantly — night as well as day — given off' by the ground, and that dew on grass, 
and on bodies close to the ground, is part of this rising vapour trapped by their 
cold surfaces. 

Curiously enough, history here repeats itself. The theory that dew rises 
from the ground has before now been wrecked by the observation that dew forms 
on bodies placed high above the ground, and in situations where no vapour 
could have risen to them from beneath. Professor Musschenbroek rejected 
Gersten's theory of rising dew after he found dew was deposited on bodies 
placed on the leaden roof of his observatory. He thought the dew formed 
under those conditions could not have risen from the ground, but must have 
fallen from the atmosphere. There must, therefore, evidently be a foundation 
somewhere for the rejection of the theory on the grounds stated, though it must 
be admitted it is difficult to find, as the statements are in no way opposed to 
each other. It will, therefore, be as well for us to consider here the cause of 
this appearance of opposition. 

One cannot help thinking that a good deal of the difficulty experienced in 



MR JOHN AITKEN ON DEW. 55 

• 

reconciling the statement, that the dew formed on bodies near the surface of 
the earth is formed of vapour rising from the ground, with the fact that dew is 
found on bodies high up in the air is caused by a want of clearness in our 
ideas, or perhaps rather to a persistence of primitive ideas. Dew was in olden 
times often spoken of as falling from the heavens, and even yet we talk of 
falling dew. This expression is to a certain extent associated with the idea of 
falling rain — a process in which the moisture passes from place to place through 
the air, and falls on bodies exposed to it ; and many seem to think that if dew 
comes out of the ground it should be found only on bodies exposed to the earth. 
That in fact rising dew is the converse of the old falling dew, whereas clew is 
only so much moisture taken by a cold surface from the store of vapour in the 
air. This explanation of the difficulty does seem somewhat absurd, but we all 
know that old habits of thought have a curious way of asserting themselves, 
and it seems the only way of explaining a difficulty so many have felt. 

Let us picture an imaginary state of matters, in which all the conditions shall 
be as simple as possible. Suppose the vapour to be constantly rising from the 
ground, and that the air is absolutely still ; and further, let us imagine that the 
vapour flows upwards through the air in a continuous stream, only varying in 
velocity at different hours. At 6 p.m. we will suppose the molecules of vapour 
that left the earth at 6 a.m. to have arrived at a height a. Let dew now begin 
to form, then the moisture condensed at 6 p.m., on bodies at the height a, will 
be vapour that rose from the ground at 6 a.m., and bodies at intermediate heights 
will have the vapour on them that rose at the intermediate hours. At 6 a.m. 
the following morning the vapour that rose at 6 on the previous evening will 
be at an elevation h, and the dew forming on all bodies lower than b at this hour 
will be vapour that rose during the night. So that in these ideal conditions, if 
we knew the rate of ascent of the vapour, we could tell the hour at which the 
vapour — condensed at any height — rose from the ground. 

If this imaginary condition of matters was correct, then there would be 
some reason for expecting that dew would only be deposited on bodies placed 
over such areas as yield vapour. In nature, however, the conditions are much 
more complicated. The vapour does not flow upwards in a uniform stream, but 
is mixed with the air by eddies and wind currents, and carried to bodies far 
from where it rose ; so that while we can say something about the source of the 
vapour condensed on bodies near the surface of the earth, yet the molecules in 
the higher air have no history we can interpret. While the vapour rising from 
the ground plays an important part in the phenomena of dew, as it is not 
only the source of that formed on bodies near the ground, but it also increases 
the amount deposited on bodies high up, yet the rising vapour is not essential 
to its formation, as dew may be deposited even though the country for many 
miles all round is dry and incapable of yielding any vapour. In such case 



56 MR JOHN AITKEN ON DEW. 

the supply of vapour to form dew would depend on the evaporation of the 
dew, and on what was brought in by the winds. 

The "Dew-Drop." 

The statement that the "dew-drops" formed on plants at night is not dew 
at all, but is formed of the exuded sap of the plant, has been rejected by some 
on account of its being contrary to all accepted ideas on the subject, while some 
who have accepted it, have given only an indifferent assent. It has therefore 
seemed desirable that further evidence be advanced in support of the state- 
ment, and also that some simpler methods be devised for studying the pheno- 
mena connected with the exudation of moisture by plants, so that those not 
accustomed to making difficult experiments may be able to demonstrate the 
point for themselves. 

One of the simplest experiments of this kind is to cut a piece of turf, or, 
better still, lift a single grass plant with a clod of earth attached to it, which 
can generally be easily found in any garden. The leaves and stems of a single 
plant being separate and open, the phenomena are more easily observed on it 
than in the confused vegetation of a turf. Place the plant on a plate, and 
invert a tumbler or other vessel over it, so as to enclose the plant and rest it on 
the plate. This should be done when the soil is not too dry, otherwise water 
will require to be given to the plant. After it has been kept in moist air 
for about an hour drops will begin to exude, and the tip of nearly every 
blade will be found to be studded with a diamond-like drop. 

In the above simple experiment there is nothing to tell us where the 
moisture came from to form the drops. It might be contended that it was 
condensed by the plant out of the moist air. It has, however, been shown in 
the first part of this paper, that when the tip of the blade is isolated from 
all supply of moist air, the drop at the end grows as quickly as the drops 
at the ends of the blades exposed to saturated air. This experiment is, 
however, a somewhat difficult one for any one not accustomed to work of 
this kind. The point may, however, be proved in a much simpler way. Take 
any exuding plant with a single stem, such as a broccoli or poppy, if it is grow- 
ing in a pot so much the better, as it is more convenient both for making and 
seeing the results of the experiment. Prepare a circular disc of metal — say tin- 
plate — with a hole in its centre large enough for the stem of the plant to pass 
through, then cut the disc in two through the centre. Now place the disc on 
the pot with the stem of the plant passing through the hole, and join the two 
halves of the disc, either by soldering, or by cementing over the joint a strip of 
sheet india-rubber. A large glass receiver is now placed over the plant with 
its edges resting on the metal plate. In this way the plant is isolated in air 
from which it can extract no moisture, the metal plate preventing vapour 



MR JOHN AITKEN ON DEW. 57 

rising from the soil underneath. If any drops now appear on the leaves, it is 
evident the air cannot be the source of the moisture. 

When tested in this way, it will be found that any exuding plant will soon 
become studded with drops, and present exactly the appearance it would at 
night. The time the drops take to appear depends on certain conditions ; 
amongst these are — 1st, the kind of plant experimented on; 2nd, the state of 
vital activity in the plant at the time ; and 3rd, the degree of dryness of the 
leaves at the time it is put under the receiver. If the leaves are very dry, it 
will take some time to fill the tissues of the plant with sap before the surplus 
begins to exude. A broccoli plant in fair health and condition may be expected 
to show drops in less than an hour. These drops are small at first, and 
gradually grow so large that they fall off by their own weight. 

An experiment of this kind is so easily made by any one, that the interest and 
the information gained is ample reward for the little trouble taken in making 
it. Instead of using a metal plate as above described for isolating the plant 
from the damp soil, a simpler plan is to use a piece of sheet india-rubber, with 
a radial slit in it, for slipping it round the plant, the two edges being joined 
with india-rubber solution, the glass receiver being, as before, placed over the 
plant, and its edges resting on the rubber. 

The evidence advanced in the first part of this paper in support of the 
statement that the " dew-drop " is exuded by the plant is — 1st, that the drop 
at the tip of a blade of grass grows as quickly when isolated from all supply of 
moist air as when exposed to saturated air ; 2nd, the blades of those plants 
which have drops attached to them on dewy nights exhibit no drops when 
separated from the root, even when supplied with water and placed in 
saturated air ; and 3rd, when hydrostatic pressure is applied to the stalk of 
the leaf of any plant that has drops attached to it at night, it causes the leaf 
to exude at exactly the same points as the drops appeared on dewy nights. 
Although the above evidence is fairly conclusive, yet there is a point where it 
might be strengthened by the addition of a link to the chain. While it is 
shown that hydrostatic pressure will produce the same effects as are seen on 
plants at nights, yet no evidence is adduced to show that there is any internal 
pressure in those plants on which " dew-drops " have been observed. This 
omission has now been corrected, and some experiments made in connection 
with this point. The plants selected for experiment were of the same kinds 
as those which were observed to have " dew-drops " on them at night, and 
which showed exuded drops when subjected to hydrostatic pressure, such as 
broccoli, cauliflower, poppy, &c. For convenience, some plants were grown in 
flower pots, and the experiments made while they were still small. 

For measuring the pressure inside the plants, U-shaped tubes half filled 
with mercury were used, and the pressure measured by the height to which 

VOL. XXXIII. PART I. H 



58 MR JOHN AITKEN ON DEW. 

the sap forced the mercury. These gauges did their work well enough, but 
they were somewhat slow in action, as it takes some time for sufficient liquid 
to be exuded to displace the mercury and force it up the tube. Where high 
pressures were required to be measured, the U tubes had to be abandoned, on 
account of their inconvenient height, as well as the length of time required for 
making an observation with them, and the pressures were measured by means 
of air-pressure gauges. These gauges were made of a short length of wide 
thermometer tube, having a bore of less than 1 mm. diameter, a short 
column of mercury being put in to form an index. The pressures were 
calculated from the volumes, and corrections made when necessary for 
temperature. The gauges were occasionally compared with a column of 
mercury to see that everything was correct. The pressures given cannot be 
considered correct to more than 10 mm. of mercury, but for the present purpose 
this degree of accuracy is sufficient, as the pressures are very indefinite, 
varying' with so many conditions that anything like an exact figure cannot be 
looked for in experiments of this kind. 

I shall now describe in detail an experiment made on a cauliflower, as 
it is similar to those made on other plants, of which it will only be necessary 
here to give the results. The pot containing the plant was placed on a sheet 
of metal, and a glass receiver got ready large enough to cover it entirely. The 
stalk of one of the blades was selected for making the connection between 
the pressure gauge and the plant. This stalk, while the leaf was still on it, was 
prepared for making a water-tight joint by filling up the longitudinal groove in 
its upper surface with beeswax, laid on with a slightly heated iron. The blade 
was now cut off, and the gauge attached by means of a short length of soft 
india-rubber tube ; the stalk having been made round by means of the beeswax, 
a tight joint was easily made. With the exception of this one leaf cut off, all the 
others were left untouched. The receiver was now put over the plant to stop 
evaporation from the leaves, and everything left at rest. After a short time 
the pressure was seen beginning to rise in the gauge, and drops also began to 
show themselves all round the edges of the leaves. As time went on the drops 
increased in size, and the pressure went up to 290 mm. of mercury, at which 
point it stopped. This pressure can be considered correct only for the par- 
ticular plant under the particular conditions. It simply meant that when the 
pressure rose to 290 mm., the whole of the supply of sap sent up by the root 
could find an exit by exudation. If the supply had been greater, or the 
exuding pores fewer or smaller, the pressure would no doubt have gone higher, 
and vice versa. 

The plant in the above experiment was in the same condition as it would be 
on a dewy night. All evaporation from the leaves was stopped, and transpira- 
tion having ceased, the root continued to send up its supplies of sap, first filling 



MR JOHN AITKEN ON DEW. . 59 

the tissues of the plant, and then producing an internal pressure, which forced 
the sap to escape by the exuding pores. But what is the condition of the 
tissues during day when transpiration is going on % An answer to this was easily 
obtained by removing the receiver from the plant, and allowing evaporation to 
proceed from its leaves. The result was that the pressure inside the plant fell, 
and a negative pressure took its place ; the mercury first fell in the U tube, and 
then rose on the other side. The mercury was drawn up in one case to a height 
of 140 mm., and in another plant to 180 mm., the height seeming to depend on 
the rate of evaporation, and the perfection and closeness of the tissues of the 
plant enabling it to stand a greater or less pressure before air forced its way 
inwards. We see from this that exuding plants during night, and at times when 
there is little evaporation, have an internal pressure tending to distend their 
tissues, and have a negative or external pressure during the clay tending to 
press the tissues inwards. This internal pressure may help to explain the more 
rigid appearance of the leaves of plants at night ; while the negative pressure 
or degree of vacuum produced inside the leaves by transpiration explains 
the manner in which water is taken up by cut flowers and branches of plants 
when their ends are placed in it, and it also explains something of the peculiar 
curving of leaves when withering. 

I have said that the pressure above measured inside of the cauliflower plant 
would have been much greater if the exuding pores had been less in size or 
number — that, in fact, the pressure then measured was not the maximum root 
pressure. To test this point, the plant was now cut across near the bottom of 
the stem, within two or three centimetres of the root, so removing all the leaves 
with their exuding pores ; and the pressure gauge was attached to the stem 
near the root. The gauge now rose very rapidly, and in a short time indicated 
a maximum pressure of 760 mm., the india-rubber connecting tube requiring to 
be strongly bandaged to prevent it bulging. It seems strange that the delicate 
tissues of a young plant should be able to produce and resist so great a pressure. 
We must however remember that this last registered pressure is one to which 
the plant is never subjected when under natural conditions, but even the 290 
mm. measured when the plant was exuding freely does seem a great pressure 
to exist in plants. 

A poppy tested in the same way showed an internal pressure of 175 mm. 
with its leaves all on, and exuding freely in saturated air. This lower pressure 
compared to the cauliflower, would seem to indicate that the exuding pores are 
larger or more numerous in the poppy than in the cauliflower, as the former are 
fully as wet as the latter on dewy nights. When the poppy was cut across, 
and the gauge attached to the main stern near the root, the pressure rose 
to as much as 1040 mm. 

The pressure inside grass has not been easily measured, owing to the diffi- 



60 MR JOHN AITKEN ON DEW. 

cult}- of making a tight joint with the gauge, and so delicate a structure as a 
grass stem. The highest pressure observed before the joint gave way was 160 
mm. The measurement was taken with all the blades on, and exuding freely in 
saturated air. This pressure is just a little less than was found in the poppy 
when under similar conditions. No measurements have been made with all 
exudation stopped, on account of grass not growing in a form suitable for 
making a measurement of this kind. 

The following are a few readings of the maximum root pressure given by 
different plants. These plants were small and still in the seed-bed, but too 
large for transplanting. 

Cauliflower, .... 875 mm. 
.... 920 „ 

.... 1065 „ 

Cabbage, .... 1310 „ 

From the above figures it will be seen that the pressures given by the 
different cauliflower plants varied considerably ; and that the cabbage experi- 
mented on was capable of exerting a root pressure equal to forcing its sap to 
a height of about 58 feet, thus showing an extraordinary reserve of energy. 

It was shown in the first part of this paper that the leaves of these plants 
exuded when hydrostatic pressure was applied to their stalks, and we have 
now shown that there is abundance of pressure inside these plants at night to 
produce the exudation. Nothing like an attempt, however, has been made here 
to give either the exact pressure inside different kinds of plants or the pressure 
under different conditions. It has already been stated that the conditions 
affecting the pressure are much too varied for the figures to be settled by a 
few experiments ; all that has been attempted is to show that in exuding plants, 
there is abundance of pressure to produce the results claimed. 

In connection with this subject, it was interesting to notice the variation in 
the exudation of grass during the late continuance of dry weather. While the 
soil was clamp exudation went on as usual, but when the ground got drier the 
exudation gradually got less and less, and at last it entirely ceased. Even when 
the grass was covered with an enclosure, and surrounded with saturated air, 
no exudation took place, and yet the grass was green and growing ; it took 
some time after the grass was wetted before the activity was great enough to 
give rise to exudation. During this dry weather, while the grass had ceased to 
exude, it got moist at nights with the hot vapour rising from the ground, the 
lower parts, particularly where exposed to radiation, being wetter than the tops 
of the blades. 

It is very difficult to get an idea of the number of plants that exude, so 
much depends on the vitality of the plant at the time, and on the amount of 



MR JOHN AITKEN ON DEW. . 61 

moisture in the ground, so that the same plant may emit droj)s at one time and 
not at another. We have seen that even so free an exuding plant as grass may 
cease to discharge ; others cease with a less degree of dryness, and with a 
less decrease in vital activity. The number that exudes under favourable 
conditions is, however, much greater than we might at first imagine. In the 
south of France, in spring, a very great number of plants were observed to 
exude on dewy nights ; even roses had their leaves fringed with drops, a 
condition in which I have never seen these plants in this country ; but the 
activity of vegetable life in spring is very much greater in the south than with us. 
This question of root pressure in plants is one of vast interest ; so much 
still remains to be known about it. How is it that one plant must have the 
soil in which it grows full of water, while another requires it to be only damp % 
Another seems to be able to grow on nearly dry soil, whilst another still can by 
means of its air-roots extract moisture from air that is not saturated. What is 
the source of energy called into action by this latter class to enable it to 
condense the vapour in the air ? Is it a chemical process ? or a purely physical 
one, like the condensation of vapour by Professor Tait's hygrometer when it 
is falling % or is it some unknown function of vitality % These questions, how- 
ever, open up a field much too wide to be considered here. 

28th July 1886. — After I had written the above paragraph, and as I supposed 
had closed the paper, it slowly dawned upon me that the surface of the leaves of 
all the different kinds of plants that have been observed to exude drops behaved 
themselves in a particular manner towards water. None of them seemed to be 
wetted by it. The glistening rain-drop on the grass shows that the blades of 
that plant are not wetted by water, the glistening being due to the reflection 
from the inside of the drop, where it rests on the blade, but does not touch it. 
But do all the other exuding plants repel water in the same manner ? As it 
was raining while these thoughts passed through my mind, a visit to the garden 
was at once made, and the broccoli, poppy, and all the other exuding plants were 
examined. Every one of them was found to behave towards the rain-drops in 
the same manner as the grass. The rain-drops slipped off their surfaces " like 
water off a duck's back ;" and where water collected in the hollows of the blades, 
the reflection from its internal surface showed it was not in contact with them. 

The other plants — cultivated and uncultivated — in the garden were then 
examined, when most of them were found to be quite wet. The difference 
in their appearance from the exuding ones was very marked. At first sight 
the leaves of plants that got wet, like potatoes, beans, &c, looked almost as if 
they were dry, but in reality the water wetted them so perfectly all over, that 
it ran off, leaving only a thin and even film on their surfaces ; whereas all 
the plants that exuded drops had their surfaces dry, save certain small areas 



G2 MR JOHN AITKEN ON DEW. 

where the natural surface of the blade had been destroyed. On thinking over the 
matter, it became evident that this property of leaves that exude drops at night 
ought to have been foreseen by me. The fact that the emitted moisture remains 
as a drop, shows that the surface of the leaf rejects water; if the leaf surface 
got wetted with water, the exuded liquid would have crept outwards from the 
exuding pore, and have wetted the leaf for some distance all around it. These 
exuded drops behave very much in the same manner as a drop of water 
attached to the end of a glass rod that is not very clean ; the water does not 
wet the rod, but draws itself up into a drop. If the drop had been attached to 
a wooden rod or a piece of thread, or anything that was easily wetted, it would 
not have remained as a drop, but have spread itself all over the surface of the 
body. 

When examining the plants in the garden during rain, in addition to those 
plants which I knew exuded drops at night, I noticed a number of others 
that rejected the rain drops, and kept their surfaces dry in the same manner as 
the exuding plants. Amongst these were Nasturtium, some of the Brassiceae 
family not previously observed, and also some weeds. Now, it appeared that if 
the above reasoning is correct, these other dry-surfaced plants ought to exude 
drops, I therefore marked them, and on afterwards experimenting found that 
they also discharged drops like the others. 

It almost looked at first sight as if this property of repelling water was a 
distinguishing characteristic of the leaves of all exuding plants; but on further 
considering the matter, the idea soon suggested itself that the other class of 
plants, the leaves of which got wetted with rain, might also exude moisture, as 
it was evident that if they did exude the discharge would be masked, for the 
moisture would not collect on them in drops, but sj)read itself over the leaves, 
and so become undistinguishable from dew. It therefore seemed desirable that 
other experiments be made on this class of plants, to see if any of them exuded 
moisture. It was evident that special precautions would be necessary to enable 
us to see the exuded moisture on leaves easily wetted, as it would not be so 
easily seen as the sparkling drop on water-repelling leaves. 

For investigating this point, the most convenient plant I could find was a 
strong growing variety of everlasting flower (Helichrysum). This plant was 
one of those observed to have its leaves wet while it was raining, and no exuded 
drops were observed on it at night. The first thing determined was to see if 
there was any root pressure to cause exudation. The plant was cut across 
at the bottom of the stem, and the pressure gauge attached near the root. The 
root pressure was found to be 950 mm.; that is, this plant had as great an 
internal pressure as was found in the drop-exuding plants. In order to see 
whether it exuded when hydrostatic pressure was applied, the upper part of 
the plant, which was cut off for taking the root pressure, was removed to the 



MR JOHN AITKEN ON DEW. . 63 

laboratory, where it was connected by means of an india-rubber tube with a 
head of water of about 15 metres, and surrounded with saturated air. After a 
time drops appeared at the tips of most of the leaves, and also at some other 
points on them ; but these drops were quite unlike those on grass, broccoli, and 
other water-repelling plants ; they spread themselves on the leaves, and adhered 
to them, no reflection being given from the back of the flattened drop. It 
could, however, be easily seen, when the experiment was made in this way, that 
moisture is exuded from the plant, whereas at night no exuded moisture is 
perceptible. The reason for this is, that under the condition of the experiment, 
the exuded drop only spreads to a certain extent, and the outline of the wetted 
surface is defined, because the whole surface of the leaf is not wet ; but at night 
the surface of the leaf is wet with dew, and the exuded drop spreads and 
thins away by imperceptible degrees into the dewed surface. This was 
illustrated in the above experiment by breathing on the leaf, so as to bring it 
into the same condition it is on dewy nights, the drop was then seen to spread 
rapidly outwards. 

We see from the above that a plant may be exuding, and yet we may not be 
able to notice it. This is specially the case while dew is forming, that is under 
natural conditions ; for dew is very generally forming while plants are exuding, 
and it is difficult to tell from an examination made at night whether any plant 
whose leaves have an affinity for water is exuding or not. It is therefore much 
better to test the plants under artificial conditions, by placing them in saturated 
air, but where no dew can be formed on their surfaces. This can be done by 
placing them at night under hand-glasses, and well protected from radiation, or 
even during the day under metal boxes, and well shaded. In this way a few 
plants, whose leaves got wet with rain, were tested, and all were found to exude 
if the evaporation from the leaves was stopped long enough, and time given for 
the tissues to get filled with sap. In all cases the exuded moisture adhered to 
the leaf and formed a wet patch. The plants tested were helichrysum, stocks, 
asters, mignonette, foxglove, celery, lettuce, turnips. 

The plants were taken at hazard, and while some, such as mignonette and 
stocks, exuded little, the others discharged a good deal. The root pressure of a 
stock was measured, and found to be only about one-half that of the more freely 
exuding Helichrysum. The root pressure will, however, be only one factor in 
determining the amount exuded, as it is evident the rate of supply sent in by 
the root will be of as much importance ; but no measurements of quantity have 
been made by me. It may be as well to note here, that though the few plants, 
taken at hazard, all showed powers of exuding, yet we must not therefore 
conclude that all plants have this property. 

It is interesting to note the effects of these two ways in which the surface 
of leaves behave towards their exuded sap and water. Take the different kinds 



64 MR JOHN AITKEN ON DEW. 

of turnips, for instance. The Swedish variety exudes freely, the liquid forming 
little drops fringing the leaves, while the moisture exuded by the other varieties 
spreads itself over the leaves. One result of this is, that after dewy nights the 
softer varieties dry sooner than the Swedish, because the exuded moisture, by 
spreading itself over the surface of the leaves, dries up much more quickly 
than the drops on the others. This seems to be the explanation of a fact fre- 
quently observed by sportsmen and others who have occasion to walk through 
turnip fields on autumn mornings, namely, that the softer varieties generally 
wet them much less than the swedes. Again, after rain the swedes take longer 
to dry than the others, because their surfaces do not get wet, but the water col- 
lects in drops, imperfectly attached to them, and also fills the hollows of their 
leaves ; whereas the other kinds get wet, and the water runs off them, leaving 
only a thin film on their surface, which dries up much more quickly than the 
drops on the others. Further, when we walk through turnips immediately after 
rain, our feet brush the drops from the swedes in showers, which rapidly wet 
us, while the water adheres to and does not so easily leave the surfaces of the 
others. 

This last part of the investigation takes us a step further, and shows us that 
not only is the dew-drop a result of the vitality of those plants on which it 
forms, but that much of the wetness spread over the leaves of others on dewy 
nights is produced by moisture exuded by the plants. 



( 65 ) 



III. — On the Foundations of the Kinetic Theory of Gases. By Professor Tait. 

(Kevised May 14, 1886.) 



INDEX TO CONTENTS. 



Introductory, . 

Part I. OneSetof Equal Spheres, §§ 1-5, . 
,, II. Mean Free Path among Equal 

Spheres, §§6-11, 
,, III. Number of Collisions per Particle 
per Second, §§ 12-14, . 
Clerk-Maxwell's Theorem,§§ 15-22, 
Rate of Equalisation of Average 
Energy per Particle in two 
Mixed Systems, §§ 23, 24, 



IV. 
V. 



PAGE 

65 
67 

71 

75 

77 



82 



Part VI. On some Definite Integrals, 

§§ 25-27, . . .84 

,, VII. Mean Path in a Mixture of 

two Systems, § 28, . .86 

,, VIII. Pressure in a System of 
Colliding Particles, §§ 29, 
30, . . . .86 

,, IX. Effect of External Potential, 

§§31,32, . . .91 

Appendix, . . . .95 



The attempt to account for the behaviour of gases by attributing their 
apparently continuous pressure to exceedingly numerous, but nearly infinitesi- 
mal, impacts on the containing vessel is probably very old. It certainly occurs, 
with some little development, in Hooke's tract of 1676, Lectures de potentid resti- 
tutivd, or of Spring ; and, somewhat more fully developed, in the Hydrodynamica 
of D. Bernoulli, 1738. Traces of it are to be found in the writings of Le Sage 
and Prevost some 80 or 90 years ago. It was recalled to notice in 1847 by 
Herapath in his Mathematical Physics, and applied, in 1848, by Joule to the 
calculation of the average speed of the particles in a mass of hydrogen at 
various temperatures. Joule expressly states 4 ' r that his results are independent 
of the number of the particles, and of their directions of motion, as also of their 
mutual collisions. 

In and after 1857 Clausius greatly improved the treatment of the problem 
by taking account not only of the mutual impacts of the particles but also of the 
rotations and internal vibrations which they communicate to one another, with 
the bearing of this on the values of the specific heats ; at the same time intro- 
ducing (though only to a limited extent) the statistical method. In this series of 
papers we find the first hint of the length of the mean free path of a particle, 
and the explanation of the comparative slowness of the process of diffusion of 
one gas into another. But throughout it is assumed, so far as the calculations 

* The paper is reprinted Phil. Mag. 1857, II. See especially p. 215. 
VOL. XXXIII. PART I. I 



66 PROFESSOR TAIT ON THE 

are concerned, that the particles of a gas are all moving with equal speeds. 
Of the Virial, which Clausius introduced in 1870, we shall have to speak 
later. 

In the Philosophical Magazine for 1860 Clerk-Maxwell published his 
papers on the " Collisions of Elastic Spheres," which had been read to the 
British Association in the previous year. In this very remarkable investigation 
we have the first attempts at a numerical determination of the length of the 
mean free path. These are founded on the observed rate of diffusion of gases 
into one another ; and on the viscosity of gases, which here first received a 
physical explanation. The statistical method is allowed free play, and conse- 
quently the law of distribution of speed among the impinging particles is 
investigated, whether these be all of one kind or a mixture of two or more 
kinds. One of his propositions (that relating to the ultimate partition of energy 
among two groups of colliding spheres), which is certainly fundamental, is 
proved in a manner open to very grave objections : — not only on account of the 
singular and unexpected ease with which the proof is arrived at, but also on 
account of the extraordinary rapidity with which (it seems to show) any forced 
deviation from its conclusions will be repaired by the natural operation of the 
collisions, especially if the mass of a particle be nearly the same in each 
system. As this proposition, in the extended form given to it by Boltzmann 
and others, seemed to render the kinetic theory incapable of explaining certain 
well-known experimental facts, I was induced to devote some time to a careful 
examination of Maxwell's proof (mainly because it appears to me to be the 
only one which does not seem to evade rather than boldly encounter the real 
difficulties of the question *), with the view of improving it, or of disproving 
the theorem, as the case might be. Hence the present investigation, which has 
incidentally branched off into a study of other but closely connected questions. 
The variety of the traps and pit-falls which are met with even in the elements 
of this subject, into some of which I have occasionally fallen, and into which I 
think others also have fallen, is so great that I have purposely gone into 
very minute detail in order that no step taken, however slight, might 
have the chance of escaping criticism, or might have the appearance of an 
attempt to gloss over a real difficulty. 

The greater part of the following investigation is concerned only with the 
most elementary parts of the kinetic theory of gases, where the particles are 

* Compare another investigation, also by Clekk-Maxwell but based on Boltzmann's processes, 
which is given in Nature, viii. 537 (Oct. 23, 1873). Some remarks on this will be made at the end of 
the paper. Meanwhile it is sufficient to point out that this, like the (less elaborate) investigations of 
Meteb and "Watson, merely attempts to show that a certain state, once attained, is permanent. It gives 
no indication of the rate at which it would bo restored if disturbed. As will be seen later, I think that 
thi.3 " rate " is an element of very great importance on account of the reasons for confidence (in the 
general results of the investigation) which it so strikingly furnishes. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 67 

regarded as hard smooth spheres whose coefficient of restitution is unity. The 
influence of external forces, such as gravity, is neglected; and so is that of 
internal (molecular) forces. The number of spheres is regarded as extremely 
great (say of the order 10 20 per cubic inch) : but the sum of their volumes is 
regarded as very small in comparison with the space through which they are 
free to move; as, for instance, of the order 10" 3 or 10~ 4 . It will be seen that 
several of the fundamental assumptions, on which the whole investigation rests, 
are justified only by reference to numbers of such enormous magnitude, or such 
extreme minuteness, as the case may be. The walls of the containing vessel 
are supposed simply to reverse the normal velocity of every sphere impinging 
on them. 

I. One set of Equal Spheres. 

1. Very slight consideration is required to convince us that, unless we 
suppose the spheres to collide with one another, it would be impossible to apply . 
any species of finite reasoning to the ascertaining of their distribution at each 
instant, or the distribution of velocity among those of them which are for the 
time in any particular region of the containing vessel. But, when the idea of 
mutual collisions is introduced, we have at once, in place of the hopelessly com- 
plex question of the behaviour of innumerable absolutely isolated individuals, 
the comparatively simple statistical question of the average behaviour of the 
various groups of a community. This distinction is forcibly impressed even 
on the non-mathematical, by the extraordinary steadiness with which the 
numbers of such totally unpredictable, though not uncommon, phenomena as 
suicides, twin or triple births, dead letters, &c, in any populous country, are 
maintained year after year. 

On those who are acquainted with the higher developments of the mathe- 
matical Theory of Probabilities the impression is still more forcible. Every one, 
therefore, who considers the subject from either of these points of view, must 
come to the conclusion that continued collisions among our set of elastic spheres 
will, provided they are all equal, produce a state of things in which the per- 
centage of the whole which have, at each moment, any distinctive property 
must (after many collisions) tend towards a definite numerical value ; from 
which it will never afterwards markedly depart. 

This principle is of the utmost value, when legitimately applied; but the 
present investigation was undertaken in the belief that, occasionally at least, its 
powers have been to some extent abused. This appears to me to have arisen 
from the difficulty of deciding, in any one case, what amount of completeness or 
generality is secured when the process of averaging is applied in successive 
steps from the commencement to the end of an investigation, instead of being 
reserved (as it ought to be) for a single comprehensive step at the very end. 



68 PROFESSOR TAIT ON THE 

Some of the immediate consequences of this principle are obvious without 
calculation: such as 

(a) Even distribution, at any moment, of all the particles throughout the 
space in which they move. 

(/;) Even distribution of direction of motion among all particles having any 
one speed, and therefore among all the particles. 

(<•) Definite percentage of the whole for speed lying between definite 
limits. 

These apply, not only to the whole group of particles but, to those in any 
portion of space sufficiently large to contain a very great number of particles. 

(d) When there are two or more sets of mutually colliding spheres, no one 
of which is overwhelmingly more numerous than another, nor in a hopeless 
minority as regards the sum of the others, similar assertions may be made as 
to each set separately. 

2. But calculation is required in order to determine the law of grouping 
as to speeds, in (c) above. It is quite clear that the spheres, even if they once 
had equal speed, could not possibly maintain such a state. [I except, of 
course, such merely artificial distributions as those in which the spheres are 
supposed to move in groups in various non -intersecting sets of parallel lines, 
and to have none but direct impacts. For such distributions are thoroughly 
unstable ; the very slightest transverse impact, on any one sphere, would at 
once upset the arrangement.] For, when equal smooth spheres impinge, 
they exchange their velocities along the line of centres at impact, the other 
components being unchanged ; so that, only when that line is equally inclined 
to their original directions of motion, do their speeds, if originally equal, remain 
equal after the completion of the impact. And, as an extreme case, when two 
spheres impinge so that the velocity of one is wholly in the line of centres at 
impact, and that of the other wholly perpendicular to it, the first is brought to 
rest and the second takes the whole kinetic energy of the pair. Still, what- 
ever be the final distribution of speeds, it is obvious that it must be in- 
dependent of any special system of axes which we may use for its computation. 
This consideration, taken along with (b) above, suffices to enable us to find this 
final distribution. 

3. For we may imagine a space-diagram to be constructed, in which lines 
arc laid off from an origin so as to represent the simultaneous velocities of all 
the spheres in a portion of space large enough to contain a very great number 
of them. Then (b) shows that these lines are to be drawn evenly in all direc- 
tions in space, and (c) that their ends are evenly distributed throughout the 
space between any two nearly equal concentric spheres, whose centres are at 
the common origin. The density of distribution of the ends (i.e., the number 
in unit volume of the space-diagram) is therefore a function of r, that is, of 



FOUNDATIONS OF THE KINETIC THEOEY OF GASES. 69 

/Jy? + y 2 + z 2 . But the argument above shows, further, that this density must 
be expressible in the form 

/(»)/<*>/<■) 

whatever rectangular axes be chosen, passing through the origin. These joint 
conditions give only two admissible results : viz., either 

f(x)=A, orf(x) = Be Cx *. 

The first is incompatible with the physical problem, as it would make the 
percentage of the whole particles, which have one definite speed, increase 
indefinitely with that speed. The same consideration shows a fortiori that, in 
the second form of solution, ivliich is the only one left, C must be negative. 
Hence the density of the distribution of " ends " already spoken of is 

If n be the whole number of particles, i.e., of "ends," we must obviously have 

/»" 

The value of the integral is 

A /!L- 

4VA 3 ' 

so that the number of spheres whose speed is between r and r + dr is 



lJMni-**i*dr (1) 



This distribution will hereafter be spoken of as the " special " state. 
The mean speed is therefore 

2 



\lVs~ 



2 rhlr = - 



while the mean-square speed is 

"V IT J Z/l 

This shows the meaning of the constant h. [Several of the results we have 
just arrived at find full confirmation in the investigations (regarding mixed 
systems) which follow, if we only put in these P for Q passim : — i.e., pass back 
from the case of a mixture of spheres of two different groups to that of a single 
group.] 

4. Meanwhile, we can trace the general nature of the process by which the 
"special" arrangement of speed expressed by (1) is brought about from any 
initial distribution of speed, however irregular. For impacts on the containing 
vessel do not alter r, but merely shift the particular " end " in question to a 



70 PROFESSOR TAIT ON THE 

different position on its spherical locus. Similarly, impact of equal particles 
does not alter the distribution of velocity along the line of centres, nor along 
any line perpendicular to it. But it does, in general, produce alterations in 
the distribution parallel to any line other than these. 

Hence impacts, in all of which the line of centres is parallel to one common 
line, produce no change in the arrangement of velocity-components along that 
line, nor along any line at right angles to it. But there will be, in general, 
changes along every other line. It is these which lead gradually (though very 
rapidly) to the final result, in which the distribution of velocity-components is 
the same for all directions. 

When this is arrived at, collisions will not, in the long run, tend to alter it. 
For then the uniformity of distribution of the spheres in space, and the 
symmetry of distribution of velocity among them, enable us (by the principle 
of averages) to dispense with the only limitation above imposed ; viz., the 
parallelism of the lines of centres in the collisions considered. 

5. In what precedes nothing whatever has been said as to the ratio of the 
diameter of one sphere to the average distance between two proximate spheres, 
except what is implied in the preliminary assumption that the sum of the 
volumes of the spheres is only a very small fraction of the space in which they 
are free to move. It is probable, though not (so far as I know) thoroughly 
proved, that if this fraction be exceedingly small the same results will ulti- 
mately obtain, but only after the lapse of a proportionately long time ; while, if 
it be infinitely small, there will be no law, as there will be practically no colli- 
sions. On the other hand, if the fraction be a large one {i.e., as in the case of 
a highly compressed gas), it seems possible that these results may be true, at 
first, only as a very brief time-average of the condition of the spheres in any 
region large enough to contain a great number : — that, in fact, the distribution 
of particles and speeds in such a region will be for some time subject to con- 
siderable but extremely rapid fluctuations. Reasons for these opinions will 
be seen in the next section of the paper. But it must also be noticed that 
when the particles fill the greater part of the space in which they move, 
simultaneous impacts of three or more will no longer be of rare occurrence ; 
and thus a novel and difficult feature forces itself into the question. 

Of course with infinitely hard spheres the probability of such multiple 
collisions would be infinitely small. It must be remembered, hoAvever, that the 
investigation is meant to apply to physical particles, and not to mere mathe- 
matical fictions ; so that we must, in the case of a highly compressed gas, take 
account of the possibility of complex impacts, because the duration of an 
impact, though excessively short, is essentially finite. 



FOUNDATIONS OF THE KINETIC THEOKY OF GASES. 71 

II. Mean Free Path among Equal Spheres. 

6. Consider a layer, of thickness Sx, in which quiescent spheres of diameter 
s are evenly distributed, at the rate of n x per unit volume. If the spheres were 
opaque, such a layer would allow to pass only the fraction 

l—n 1 irs 2 Sx/4 : 

of light falling perpendicularly on it. But if, instead of light, we have a group 
of spheres, also of diameter s, falling perpendicularly on the layer, the fraction 
of these which (whatever their common speed) pass without collision will 
obviously be only 

1 — n-^Tr.^Sx ; 

for two spheres must collide if the least distance between their centres is not 
greater than the sum of their radii. It is, of course, tacitly understood when 
we make such a statement that the spheres in the very thin layer are so scattered 
that no one prevents another from doing its full duty in arresting those which 
attempt to pass. Thus the fraction above written must be considered as 
differing very little from unity. In fact, if it differ much from unity, this 
consideration shows that the estimate of the number arrested will necessarily 
be exaggerated. Another consideration, which should also be taken into 
account is that, in consequence of the finite (though very small) diameter of the 
spheres, those whose centres are not in the layer, but within one diameter of it, 
act as if they were, in part, in the layer. But the corrections due to these 
considerations can be introduced at a later stage of the investigation. 

7. If the spheres impinge obliquely on the layer, we must substitute for hx 
the thickness of the layer in the direction of their motion. 

If the particles in the layer be all moving with a common velocity parallel to 
the layer, we must substitute for Sx the thickness of the layer in the direction 
of the relative velocity. 

If the particles in the layer be moving with a common velocity inclined at 
an angle ^ — 6 to the plane of the layer, and the others impinge perpendicularly 
to the layer, the result will be the same as if the thickness of the layer were 
reduced in the ratio of sin 6 : 1, and it were turned so as to make an angle 6 
with the direction of motion of the impinging particles. 

8. Now suppose the particles in the layer to be moving with common speed 
v u but in directions uniformly distributed in space. Those whose directions of 
motion are inclined at angles between (3 and /3 + dfi to that of the impinging 

particles are, in number, 

?i 2 sin /3^/3/2 ; 

and, by what has just been said, if v be the common speed of the impinging 



72 PROFESSOR TAIT ON THE 

particles, the virtual thickness of the layer (so far as these particles are con- 
cerned) is 

v Sx/v, 



where v = Jv 2 +v j 2 —2w 1 cos[3 

is the relative speed, a quantity to be treated as essentially positive. 

Thus the fraction of the impinging particles which traverses this set without 
collision is 

1 — i^tts^SxVq sin /3 d/3/2v . 

To find the fraction of the impinging particles which pass without collision 
through the layer, we must multiply together all such expressions (each, of 
course, infinitely nearly equal to unity) between the limits and -k of {3. The 
logarithm of the product is 



?2. 1 7TS 2 &£ 



]xT" 

-/ sjv 2 +v 1 2 — 2vv x cos/3. sin /3cl/3> 



2v 
Making v the variable instead of /3, this becomes 






2v\J u ° dv °- 

If v be greater than v u the limits of integration are v — v lf and v + i\, and the 
expression becomes 

1 + 3F 2 )' 
but, if v be less than v u the limits are Vi — v and v x + v, and the value is 

-**<£+?)• 

These give, as they should, the common value 

— 4» 1 7ts 2 &/3 
when v=Vi. 

9. Finally, suppose the particles in the layer to be in the " special" state. 

If there be n in unit volume, we have for the number whose speed is between 

the limits Vi and v 1 + dv 1 

n^invfdv^-'' ' 



-6 

7T 



Hence the logarithm of the fraction of the whole number of impinging particles, 
whose speed is v and which traverse the layer without collision, is 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 73 

The value of the factor in brackets is easily seen to be 

_dj l&V (to 1\ 

dh "*" 3v 2 dh 2 ^\3h^~ 2h 2 v) £ ' 

where v= \/ t~ hv *dv, 

and thus it may readily be tabulated by the help of tables of the error-function. 
When v is very large, the ultimate value of the expression is 



4 v ; 



77 
J? 



which shows that, in this case, the " special " state of the particles in the layer 
does not affect its permeability. 
10. Write, for a moment, 

— eSx 

as the logarithm of the fraction of the particles with speed v which traverse the 
layer unchecked, Then it is clear that 

—ex 
£ 

represents the fraction of the whole which penetrate unchecked to a distance 
x into a group in the " special " state. Hence the mean distance to which 
particles with speed v can penetrate without collision is 

/ £ xdx i 



e~ ex dx e 



/n 



This is, of course, a function of v ; and the remarks above show that it increases 
continuously with v to the maximum value (when v is infinite) 



i.e., the mean path for a particle moving with infinite speed is the same as if 
the particles of the medium traversed had been at rest. 

11. Hence, to find the Mean Free Path among a set of spheres all of which 
are in the special state, the natural course would appear to be to multiply the 

VOL. XXXIII. PART I. K 



74 PROFESSOR TAIT ON THE 

average path for each speed by the probability of that speed, and~take the 
sum of the products. Since the probability of speed v to v + dv is 

/A 3 
the above definition gives for the length of the mean free path, 







or, by the expression for e above, 



1 

mrs* 




^ , t^+i-^T , +^> 



This may without trouble (see § 9) be transformed into the simpler expression 

4afit~ xt d% 



n-n-s- I 

J § 



x e- j:i + (2x 2 + l)^''e- xi dx 



which admits of easy numerical approximation. The numerical work would be 
simplified by dividing above and below by e~ r2 , but we prefer to keep the 
present form on account of its direct applicability to the case of mixed 
systems. And it is curious to note that 4«~* 8 is the third differential coefficient 
of the denominator. 

The value of the definite integral (as will be shown by direct computation 
in an Appendix to the paper) is about 

0-677 ; 

and this is the ratio in which the mean path is diminished in consequence of 
the motion of the particles of the medium. For it is obvious, from what 
precedes, that the mean path (at any speed) if the particles were quiescent 

would be 

1 

717TS 2 

The factor by which the mean path is reduced in consequence of the 
" special" state is usually given, after Clerk-Maxwell, as I/*/ 2 or 0707. 

But this appears to be based on an erroneous definition. For if n v be 
the fraction of the whole particles which have speed v, p v their free path; we 
have taken the mean free path as 

according to the usual definition of a " mean." 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 75 

Clerk-Maxwell, however, takes it as 

*2,(n v v) 

I.(n v vjp v ) ' 

i.e., the quotient of the average speed by the average number of collisions per 
particle per second. But those who adopt this divergence from the ordinary 
usage must, I think, face the question " Why not deviate in a different direction, 
and define the mean path as the product of the average speed into the average 
time of describing a free path ? " This would give the expression 

I.(n v v) . l,(n v p v /v) . 

The latter factor involves a definite integral which differs from that above 
solely by the factor JJifx in the numerator, so that its numerical determination 
is easy from the calculations already made. It appears thus that the reducing 
factor would be about 

~X 0-650, =0734 nearly; 

i.e., considerably more in excess of the above value than is that of Clerk- 
Maxwell. Until this comparatively grave point is settled, it would be idle to 
discuss the small effect, on the length of the mean free path, of the diameters 
of the impinging spheres.] 



III. Number of Collisions per Particle per Second. 

12. Here again we may have a diversity of definitions, leading of course 
to different numerical results. Thus, with the notation of § 11, we may give 
the mean number of collisions per particle per second as 

This is the definition given by Clerk-Maxwell and adopted by Meyer ; and 
here the usual definition of a " mean " is employed. The numerical value, by 
what precedes, is 

Meyer evaluates this by expanding in an infinite series, integrating, and sum- 
ming. But this circuitous process is unnecessary ; for it is obvious that the 
two parts of the expression must, from their meaning, be equal ; while the 
second part is integrable directly. 

13. On account of its bearing (though somewhat indirectly) upon the treat- 



7l) PROFESSOR TAIT ON THE 

ment of other expressions which will presently occur, it may be well to note 
that a mere inversion of the order of integration, in either part of the above 
double integral, changes it into the other part. 

Otherwise : — we may reduce the whole to an immediately integrable form 
by the use of polar co-ordinates ; putting 

v = r cos , v x = r sin 6 , 

and noting that the limits of r are to oo in both parts, while those of 
6 are to tt/4 in the first part, and tt/4 to tt/2 in the second. [This trans- 
formation, however, is not well adapted to the integrals which follow, with 
reference to two sets of spheres, because h has not the same value in each set.] 
14. Whatever method we adopt, the value of the expression is found to be 



\Z 8 j- ns * =2 \/£h 

and, as the mean speed is (§ 3) 



7TOS- 



JttIi 

we obtain Clerk-Maxwell's value of the mean path, above referred to, viz., 

1 

?17TS 2 J2' 

But (in illustration of the remarks at the end of § 11) we might have defined 
the mean number of collisions per particle per second as 

vv v ' or as ^v -j-x ; &c, &c. 

z,(n v p v ) X{n v p v lv) 

The first, which expresses the ratio of the mean speed to the mean free path, 
gives 

2 7T71S 2 



J^h 0-677' 

and the second, which is the reciprocal of the mean value of the time of 
describing a free path, gives 

1 7TW.S 2 

Jh W65Q' 

The three values which we have adduced as examples bear to one another 
the reciprocals of the ratios of the above-mentioned determinations of the 
mean free path. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 77 



IV. Clerk- Maxwell's Theorem. 

15. In the ardour of his research of 1859, # Maxwell here and there con- 
tented himself with very incomplete proofs (we can scarcely call them more 
than illustrations) of some of the most important of his results. This is 
specially the case with the investigation of the law of ultimate partition of 
energy in a mixture of smooth spherical particles of two different kinds. He 
obtained, in accordance with the so-called Law of Avogadro, the result that the 
average energy of translation is the same per particle in each system; and he 
extended this in a Corollary to a mixture of any number of different systems. 
This proposition, if true, is of fundamental importance. It was extended by 
Maxwell himself to the case of rigid particles of any form, where rotations 
perforce come in. And it appears that in such a case the whole energy is 
ultimately divided equally among the various degrees of freedom. It has since 
been extended by Boltzmann and others to cases in which the individual 
particles are no longer supposed to be rigid, but are regarded as complex 
systems having great numbers of degrees of freedom. And it is stated, as the 
result of a process which, from the number and variety of the assumptions made 
at almost every stage, is rather of the nature of playing with symbols than of 
reasoning by consecutive steps, that in such groups of systems the ultimate 
state will be a partition of the whole energy in equal shares among the classes 
of degrees of freedom which the individual particle-systems possess. This, if 
accepted as true, at once raises a formidable objection to the kinetic theory. 
For there can be no doubt that each individual particle of a gas has a very 
great number of degrees of freedom besides the six which it would have if it 
were rigid : — the examination of its spectrum while incandescent proves this at 
once. But if all these degrees of freedom are to share the whole energy (on the 
average) equally among them, the results of theory will no longer be consistent 
with our experimental knowledge of the two specific heats of a gas, and the 
relations between them. 

16. Hence it is desirable that Clerk-Maxwell's proof of his fundamental 
Theorem should be critically examined, and improved where it may be found 
defective. If it be shown in this process that certain preliminary conditions 
are absolutely necessary to the proof even of Clerk-Maxwell's Theorem, and 
if these cannot be granted in the more general case treated by Boltzmann, it is 
clear that Boltzmann's Theorem must be abandoned. 

17. The chief feature in respect of which Maxwell's investigation is to be 
commended is its courageous recognition of the difficulties of the question. 
In this respect it far transcends all other attempts which I have seen. Those 

* Phil. Mag., 1860. 



78 PROFESSOR TAIT ON THE 

features, besides too great conciseness, in respect of which it seems objec- 
tionable, are : — 

((/) He assumes that the transference of energy from one system to the other 
can be calculated from the results of a single impact between particles, one 
from each system, each having the average translational energy of its system. 

Thus (so far as this step is concerned) the distribution of energy in each 
system may be any whatever. 

(b) In this typical impact the velocities of the impinging spheres are taken 
as at right angles to one another, so that the relative speed may be that of 
mean square as between the particles of the two systems. The result obtained 
is fallacious, because in general the directions of motion after impact are found 
not to be at right angles to one another, as they would certainly be (on account 
of the perfect reversibility of the motions) were this really a typical impact. 

(c) Clerk-Maxwell proceeds as if every particle of one system impinged 
upon one of the other system at each stage of the process — i.e., he calculates 
the transference of energy as if each pair of particles, one from each system, 
had simultaneously a typical impact. This neglect of the immensely greater 
number of particles which either had no impact, or impinged on others of their 
own group, makes the calculated rate of equalisation far too rapid. 

(d) Attention is not called to the fact that impacts between particles are 
numerous in proportion to their relative speed, nor is this consideration intro- 
duced in the calculations. 

(e) Throughout the investigation each step of the process of averaging is 
performed (as a rule) before the expressions are ripe for it. 

18. In seeking for a proof of Maxwell's Theorem it seems to be absolutely 
essential to the application of the statistical method to premise : — 

(A) That the particles of the two systems are thoroughly mixed. 

(B) That in any region containing a very large number of particles, the 
particles of each kind separately acquire and maintain the error-law distribu- 
tion of speeds — i.e., each set will ultimately be in the " special " state. The 
disturbances of this arrangement produced in either system by impacts on 
members of the other are regarded as being promptly repaired by means of the 
internal collisions in the system itself. This is the sole task assigned to these 
internal collisions. We assume that they accomplish it, so we need not further 
allude to them. 

[The warrant for these assumptions is to be sought as in § 4 ; and in the 
fact that only a small fraction of the whole particles are at any instant in 
collision; i.e., that each particle advances, on the average, through a consider- 
able multiple of its diameter before it encounters another.] 

(C) That there is perfectly free access for collision between each pair of 
particles, whether of the same or of different systems ; and that, in the mixture, 



FOUNDATIONS OF THE KINETIC THEORY OF OASES. 79 

the number of particles of one kind is not overwhelmingly greater than that of 
the other kind. 

[This is one of the essential points which seem to be wholly ignored by 
Boltzmann and his commentators. There is no proof given by them that one 
system, while regulating by its internal collisions the distribution of energy 
among its own members, can also by impacts regulate the distribution of 
energy among the members of another system, when these are not free to 
collide with one another. In fact, if (to take an extreme case) the particles of 
one system were so small, in comparison with the average distance between 
any two contiguous ones, that they practically had no mutual collisions, they 
would behave towards the particles of another system much as Le Sage 
supposed his ultra-mundane corpuscles to behave towards particles of gross 
matter. Thus they would merely alter the apparent amount of the molecular 
forces between the particles of a gas. And it is specially to be noted that this 
is a question of effective diameters merely, and not of masses : — so that those 
particles which are virtually free from the self-regulating power of mutual 
collisions, and therefore form a disturbing element, may be much more massive 
than the others.] 

19. With these assumptions we may proceed as follows: — Let P and Q be the 
masses of particles from the two systems respectively ; and when they impinge, 
let u, v be their velocity-components measured towards the same parts along 
the line of centres at impact. If these velocities become, after impact, u', v' 
respectively, we have at once 

P(u'-u)=-|^(u-v)=-Q(v'-v); 
an immediate consequence of which is 

p (u '2_ u2)= __J|Q_(p u 2_Q v 2_ ( p_Q )uv ) = _Q (v '2_ v 2 ) . 

Hence, denoting by a bar the average value of a quantity, we see that trans- 
ference of energy between the systems must cease when 

P[r 2 -Qv2-(P-Q)u^ = 0, (1), 

and the question is reduced to finding these averages. 

[I thought at first that uv might be assumed to vanish, and that u 2 and v 2 
might each be taken as one-third of the mean square speed in its system. 
This set of suppositions would lead to Maxwell's Theorem at once. But 
it is clear that, when two particles have each a given speed, they are more 
likely to collide when they are moving towards opposite parts than when 
towards the same parts. Hence uv must be an essentially negative quantity, 
and therefore Pu 2 necessarily less than Qv 2 , if P be greater than Q. Thus it 



M) PROFESSOR TAIT ON THE 

seemed as if the greater masses would have on the average less energy than 
the smaller. These are two of the pitfalls to which I have alluded. Another 
will be met with presently.] 

20. But these first impressions are entirely dissipated when we proceed to 
calculate the average values. For it is found that if we write (1) in the form 



Pu 2 — uv — Qv 2 — uv = 0, 
the terms on the left are equal multiples of the average energy of a P and 
of a Q respectively. Thus Maxwell's Theorem is rigorously true, though 
in a most unexpected manner. There must surely be some extremely simple 
and direct mode of showing that u 2 — uv is independent of the mean-square 
speed of the system of Qs. Meanwhile, in default of anything more simple, 
I give the investigation by which I arrived at the result just stated. 

21. Suppose a particle to move, with constant speed v, among a system of 
other particles in the " special " state ; the fraction of the whole of its 
encounters which takes place with particles, whose speed is from i\ to v x + dv x 
and whose directions of motion are inclined to its own at angles from 
/3 to fi + dfi, is (§ 8) proportional to 

or as we may write it for brevity 

v^v sin 6 d8 . 

This is easily seen by remarking that, by § 8, while the particle advances 
through a space hx, it virtually passes through a layer of particles (such as those 
specified) of thickness vfix/v. Here (§ 3) 3j2k is the mean-square speed of the 
• (articles of the system. 

Let the impinging particle belong to another group, also in the special 
state. Then the number of particles of that group which have speeds between 
v and v + dv is proportional to 

s- hv Vdv= v> 
as we will, for the present, write it. 

Now let V, Y v V , in the figure, be the projections of v, v v v on the 

unit sphere whose centre is ; C that of the 
line of centres at impact. Then VOVj = /3. 
Let V OV = a, VqOV! = a v V OC = y, and 
VV C = (f>. The limits of y are and n/2 ; 
those of (J> are and 2tt. Also the chance that 
C lies within the spherical surface- element 
sin ydydfy, is proportional to the area of the 
projection of that element on a plane perpen- 
dicular to the direction of v , i.e., it is proportional to 

cos y sin y dyd(p . 



/[\ 






"Stf 


/ \ 






/' 




/\ Vo 


/ 








,' 




' ^^~~~C~' 


'--. "*{ 


/v , 





IV — XXV : 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 81 

But by definition we have 

u = v cos VOC = v(cos a cos y -f sin a sin y c )S <p). 
v=v 1 cos V 1 OC = ^(cos ai cos y + sin a x sin y cos 0) ; 

and by the Kinematics of the question, as shown by the dotted triangle in the 

figure, we have 

v cos a — v l cos a 1 = v , 
vsin a — ^sin ai = . 

Thus, as indeed is obvious from much simpler considerations, 

U — V = V COS y , 

so that 

lvv^v sin /3 d{3 u(u — v) cos y sin y e?ye?0 

/wjVq sin /3 rf/3 cos y sin y rfycZ^ 

/w/^oSin/StfySv (cosacosy + sin a sin 7 cos (f>)v cos 2 7 sin 7 dyd<f> 
/vviV sin /3 d/3 cos 7 sin 7 d<yd<p 

where each of the integrals is quintuple. 

The term in cos <f> vanishes when we integrate with respect to <f> : — and, 
when we further integrate with respect to y, we have for the value of the 
expression 

^ /vv x v sin /3 d/3vv Q cos a 

Ivv-Pq sin /3 d@ 
where the integrals are triple. 
Now 

2vv cos a = v 2 + v 2 — v-f , 
and 

Wi sin (3 df3 — v dv , 

so that the expression becomes 

It will be shown below (Part VI.), that we have, generally 

/• y 2 ^^ _ Wl _ Vj (ft + fc)— 

J VVl vv x 2n + l "" 4 (M)^ 1 ' 

and that it is lawful to differentiate such expressions with regard to h or to k. 

Hence 

d d 



U' — UV : 



iVfi-U-a)v» 1 



4 I 3 /3 7. 

Thus Clerk-Maxwell's Theorem is proved. 
VOL. XXXIII. part 1. 



82 PROFESSOR TAIT ON THE 

22. The investigation of the separate values of the parts of this expression 
is a little more troublesome, as the numerators now involve second partial 
differential coefficients of I x ; but it is easy to see that we have 

- = _i \dh" til-) Tl " 2 ( 3 dh ~ dk) l * /3 + Is/5 ii + 2k 



16 I 3 /3 2h(h + k) 

- 1 a-0 I .-<a^.)v3-3i,/5 t 



uv = - T , 



16 y3 2(h + k) 

and, from these, the above result again follows. 

[It is clear, from the investigation just given, that the expression for the 
value of u 2 — uv would be the same (to a numerical factor iwes) whatever law we 
assumed for the probability of the line of centres having a definite position, 
and thus that Maxwell's Theorem would be true, provided only that the law 
were a function of y alone, and not of <f> (i.e., that the possible positions of 
the line of centres were symmetrically distributed round the direction of 
relative motion of the impinging particles). In my first non-approximate 
investigation (read to the Society on Jan. 18, and of which an Abstract 
appeared in Nature, Jan. 21, 1886) I had inadvertently assumed that the possible 
positions of C were equally distributed over the surface of the hemisphere of 
which V is the pole, instead of over the surface of its diametral plane. The 
forms, however, of u 2 and of uv separately, suffer more profound modifications 
when such assumptions are made.] 

V. Bate of Equalisation of Average Energy per particle in two 

Mixed Systems. 

23. To obtain an idea of the rate at which a mixture of two systems 
approaches the Maxwell final condition, suppose the mixture to be complete, 
and the systems each in the special state, but the average energy per particle 
to be different in the two. As an exact solution is not sought, it will be 
sufficient to adopt, throughout, roughly approximate expressions for the various 
quantities involved. We shall choose such as lend themselves most readily to 
calculation. 

It is easy to see, by making the requisite slight modifications in the formula 
of § 12, that, if m be the number of Ps and n that of Qs in unit volume, the 
number of collisions per second between a P and a Q is 

2mn W Jk J > 
where s now stands for the sum of the radii of a P and of a Q. For if, in the 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 83 

formula referred to, we put (M) 3/2 for h 3 , and also put k for h in the exponentials 
where the integration is with respect to v ly it becomes 

8ns 2 (hk)%/3 , 

according to the notation of § 21. This is the average number of impacts per 
second which a P has with Qs. 

Hence, if •& be the whole energy of the Ps, p that of the Qs, per unit volume, 
the equations of § 19 become 

16 PQ . /irQi+k), > 

from which we obtain, on the supposition (approximate enough for our purpose) 
that we may treat ljh + l/k as constant, 

where 

1_1_6_2Q_ / ! r(A+i). 

T~3 (P + Q)*^ W + w;V hk 

The quantity 

tits — mp = mn(m/m — p/n) , 

is mn times the difference of the average energies of a P and a Q, and (since 
g 4 - 6 r= 100 nearly) we see that it is reduced to one per cent, of its amount in the 

time 

t ,__ 13.8 (P + Q) 2 / hk , 

t x = 4.6T = TX - — — -. v V( ?' V n , 7 , seconds. 

24. For a mixture, in equal volumes, of two gases in which the masses of 
the particles are not very different, say oxygen and nitrogen, we may assume as 
near enough for the purposes of a rough approximation 

m = % = |xl0 20 , 

whence m + n (per cubic inch) is double of this, 

^ = 27, = (12 x 1600 inch sec.) 2 , 

s = 3x 10 -8 inch, 

so that 

13.8xl0 16 x4 /3 1 , . 

h = T7r — 7{ — r, — TKSTi — tt; — tt^t^V r~ = rr— --,-r.a seconds, nearly: 
16x9x3x 10 20 x 12x1600 4tt 3 x 10 9 ' ' 

and the difference has fallen to 1 per cent, of its original amount in this period, 
i.e., after each P has had, on the average, about four collisions with Qs. This 
calculation has no pretensions to accuracy, but it is excessively useful as showing 
the nature of the warrant which we have for some of the necessary assump- 



84 PROFESSOR TAIT ON THE 

tions made above. For if the rapidity of equalisation of average energy in two 
systems is of this extreme order of magnitude, we are entitled to suppose that 
the restoration of the special state in any one system is a phenomenon taking 
place at a rate of at least the same if not a higher order of magnitude. 

Clerk-Maxwell's result as regards the present question is that, at every 
typical impact between a P and a Q, the difference of their energies is reduced 
in the ratio 

VP+Q/ ' 
so that, if the masses were equal, the equalisation would be instantaneous. 



VI. On some Definite Integrals. 
25. It is clear that expressions of the forms 

i~ hx2 x r dx / s-Wy'dy and / g ~ hx2 x r dx / e-Wtfdy , 

J J o J X 

where r and s are essentially positive integers, may lawfully be differentiated 
under the integral sign with regard to h or to k. In fact they, and their differ- 
ential coefficients, which are of the same form, are all essentially finite. 

As, in what immediately follows, we shall require to treat of the first 
of these forms only when r is odd and s even, and of the second only when 
/• is even and s odd, it follows that their values can all be obtained by 
differentiation from one or other of the integrals 



fz~ hx2 xdx n-**dy = — ^L= 
Jo Jo J 4hjh+k 



■Jh + Jc 

and 

fir 



fl-^dx fe-Wydy = — d" 



Jh+k 

These values may be obtained at once by noticing that the second form is 
integrable directly ; while, by merely inverting the order of integration, it 
becomes the first with h and k interchanged. 

26. In §§ 21, 22 we had to deal with a number of integrals, all of one form, 
of which we take as a simple example 



^0 



Is/3=/%J- 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 85 

From the remarks above it is clear that this can be expressed as 

Sj^ffn d2 | *\ 1 ,f 2 d2 + d2 \ 1 ) 
3 4 1 \ 6 dhdk * dkV h Jh+k + [dkdh dh*J k Jh +k) 



2JirZ/ k+3h 3k+h 



+ 



-1 



"3 4 2\h 2 (h+k)^k\h+k)i 

J* ( k s +Sk Vi) + (3k7i 2 +h z ) 
4 h?k 2 (h+k)S 

- 4 (hkf ' 

The peculiar feature here shown is the making up of the complete cube 
of k 4. k in the numerator by the supply of the first half of its terms from the 
first part of the integral, and of the remainder from the second* On trial I 
found that the same thing holds for I 5 and I 7 , so that I was led to conjecture 
that, generally, as in § 21 

2«-l 

2n+l 4 ' (hk)»+ 1 

After the preliminary work we have just ''given, it is easy to prove this as 
follows. We have always 

((x+y)^-(x-y)^)((x+yy+(x-y) 2 ) = 
(x + y yn+s _ (p _ y yn+s + Qfl - y 2 y(( x+ yf n ^-(x- yf n - !) . 

Operate on this by 

Jz'^xdx J e'Wydy ( ), 

and on the same expression, with x and y interchanged (when, of course, it 
remains true), by 

Jz ~ hx -xdx I g - tfydy ( J , 

and add the results. This gives at once 

~KdJ + Mr 2n+1=l2n+3+ \dTi~dk) l2 "- a ; 

which is found on trial to be satisfied by the general value given above. 

* Prof. Catley has called my attention, in connection with this, to the following expression 
from a Trinity (Cambridge) Examination Paper : — 

{a + b) 2 " = (a+b) n (a" + b") 

+ (a + b)"~ i (na"b + nab") 

+ («+5J»-« ( n - n + 1 a"V+ V±+la'bA 
' \ 1.2 1.2 / 

+ (« + &) n - n + 1 2n - i (aPb--i +a n-i b n ) . 

1.2 .... n-1 



*»i PROFESSOR TAIT ON THE 

27. Partly as a matter of curiosity, but also because we shall require a 
case of it, it may be well to mention here that similar processes (in which it is 
no longer necessary to break the y integration into two parts) lead to the 
companion formula 



hn _ /g-A*2 xdx / g -t y 2 ydJ x + J" -x-y n 
2/i J o J o 



n-l 



= tt_ 1 .3.5. .. (2n-l) (h+k) 
~ 4 2" 2n + 1 

(Kk) 2 

And we see, by Wallis' Theorem, that (when n is increased without limit) 
I 2n is ultimately the geometric mean between !,„_! and I 2 „ +1 . 



VII. Mean Path in a Mixture of two Systems. 

28. If we refer to § 10, we see that, instead of what was there written as — ehx, 
we must now write —(e + e^Sx; where e v which is due to stoppage of a 
particle of the first system by particles of the second, differs from e in three 
respects only. Instead of the factor 4s 2 , which appears in e, we must now 
write (s + Sif; where s-^ is the diameter of a particle of the second system. 
Instead of h and n we must write h 1 and n x respectively. 

Hence the mean free path of a particle of the first system is 









which, when the values of e and e x are introduced, and a simplification 
analogous to those in §§ 9, 11, is applied, becomes 

in which 

Thus the values tabulated at the end of the paper for the case of a single 
system enable us to calculate the value of this expression also. 

VIII. Pressure in a System of Colliding Particles. 

29. There are many ways in which we may obtain, by very elementary 
processes, the pressure in a system of colliding particles. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 87 

(a) It is the rate at which momentum passes across a plane unit area ; or 
the whole momentum which so passes per second. [It is to be noted that a 
loss of negative momentum by the matter at either side of the plane is to be 
treated as a gain of positive.] 

In this, and the other investigations which follow, we deal with planes sup- 
posed perpendicular to the axis of x ; or with a thin layer bounded by two such 
planes. 

The average number of particles at every instant per square unit of a layer, 
whose thickness is Bx, is n&x. Of these the fraction 

7T 

have speeds from v to v + dv. And of these the fraction 

sin /3 d/3/2 

are moving in directions inclined from /3 to /3 + d/3 to the axis of x. Each of 
them, therefore, remains in the layer for a time 

Sx/v cos & 
and carries with it momentum 

Vv cos ft 

parallel to x. Now from /3 = to fi = ~x we have positive momentum passing 

towards x positive. From /3 = -„- to /3 = tt we have an equal amount of 

negative momentum leaving x positive. Hence the whole momentum which 
passes per second through a plane unit perpendicular to x is 

cos 2 $ sin fidfi = gPwjj 2 " 
o ~s 

where the bar indicates mean value. That is 

2 
Pressure =p — o (Kinetic Energy in Unit Volume). 

(b) Or we might proceed as follows, taking account of the position of each 
particle when it was last in collision. 

Consider the particles whose speeds are from v to v + dv, and which are con- 
tained in a layer of thickness Sx, at a distance x from the plane of yz. Each 
has (§ 10) on the average ev collisions per second. Thus, by the perfect re- 
versibility of the motions, from each unit area of the layer there start, per 

second, 

nvevSx 

such particles, which have just had a collision. These move in directions 
uniformly distributed in space ; so that 

sin j3 dfi/2 




88 PROFESSOR TAIT ON THE 

of them are moving in directions inclined /3 to /3 + cZ/3 to the axis of x. Of 
these the fraction 

—ex gee 8 

(where x is to be regarded as signless) reach the plane of yz, and each brings 

momentum 

Vv cos /5 

perpendicular to that plane. Hence the whole momentum which reaches unit 
area of the plane is 



2x 



i r r> r 

^nV/ vv 2 I cos /3 sin /3 d/3 J cdxe- exaecfi 



vv 2 I ' 

c/0 



cos 2 /3 sin /3r?/3, 



the same expression as before. 

(c) Clausius' method of the virial, as usually applied, also gives the same 
result. 

30. But this result is approximate only, for a reason pointed out in § 6 
above. To obtain a more exact result, let us take the virial expression itself. 
It is, in this case, if N be the number of particles in volume V, 

^N^^V + I^Rr), 

where R is the mutual action between two particles whose centres are ;* apart, 
and is positive when the action is a stress tending to bring them nearer to one 
another. Hence, omitting the last term, we have approximately 

which we may employ for the purpose of interpreting the value of the term 
omitted. 

[It is commonly stated (see, for instance Clekk-Maxwell's Lecture to the 
Chemical Society *) that, when the term ^(Rr) is negative, the action between 
the particles is in the main repulsive : — "a repulsion so great that no attainable 
force can reduce the distance of the particles to zero." There are grave 
objections to the assumption of molecular repulsion ; and therefore it is well to 
inquire whether the mere impacts, which must exist if the kinetic theory be 
true, are not of themselves sufficient to explain the experimental results which 
have been attributed to such repulsion. The experiments of Regnault on 
hydrogen first showed a deviation from Boyle's Law in the direction of loss 

* Cfiem. Soc. Jour., xiii. (1875), p. 4'J3. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 89 

compression than that Law indicates. But Andrews showed that the same 
thing holds for all gases at temperatures and pressures over those correspond- 
ing to their critical points. And Amagat has experimentally proved that in 
gaseous hydrogen, which has not as yet been found to exhibit any traces of 
molecular attraction between its particles, the graphic representation of pY 
in terms of p (at least for pressures above an atmosphere, and for common 
temperatures) consists of a series of parallel straight lines. If this can be 
accounted for, without the assumption of molecular repulsion but simply by 
the impacts of the particles, a real difficulty will be overcome. And it is 
certain that, at least in dealing with hard colliding spheres if not in all cases, 
we have no right to extract from the virial, as the pressure term, that part 
only which depends upon impacts on the containing vessel ; while leaving 
unextracted the part depending on the mutual impacts of the particles. The 
investigation which follows shows (so far as its assumptions remain valid when 
the particles are not widely scattered) that no pressure, however great, can 
bring a group of colliding spheres to a volume less than four times the sum of 
their volumes. If they were motionless they could be packed into a space 
exceeding the sum of their volumes in the ratio 6 : rr^/2, or about 1-35 : 1, 
only.] 

In the case of hard spheres we have obviously r = s; and, with the notation 
of § 19, remembering that Q = P, k = h, we have 

E=-P(u-v). 

Hence we must find, by the method of that section, the mean value of the 
latter expression. It is easily seen to be 

_ -afwiV* sin /3 dfi cos 2 >y sin yd<yd<j> _ 2V/vv 1 v HvJvv 1 
fvv x v^ sin ft d/3 cos 7 sin <yd<yd<f> 3 fw^o^-dv^vv^ 

2P I 4 /4 



3 I 3 /3 ~ l V 2h' 



But, § 14, the average number of collisions, per particle per second, is 

2 N 



2 f± ^ 



Hence, for any one particle, the sum of the values of E (distributed, on the 
average, uniformly over its surface) is, in one second, 

v , m 2NP , 4N _ 

2(R) = — ^v ~T3 v IWs2= -P-4**' 

Thus it would appear that we may regard each particle as being subjected to 
the general pressure of the system ; but as having its own diameter doubled. 

VOL. XXXIII. PART I. M 



90 PROFESSOR TAIT ON THE 

It is treated, in fact, just as it would then be if all the others were reduced to 
massive points. 

The value of the term in the virial is 

1 ns2(R) 

because, though every particle suffers the above average number of collisions, 
it takes two particles to produce a collision. This is equal to 

— np7rs' i = —6p (sum of volumes of spheres) ; 

so that the virial equation becomes 

o 

nVv-/2 = — p(V— 4 (sum of volumes of spheres)). 

which, inform at least, agrees exactly with Amagat's* experimental results for 
hydrogen. 

These results are closely represented at 18° C. by 

p(V- 2-6) = 2731; 
and at 100° C. by 

^(V-2-7) = 3518. 

The quantity subtracted from the volume is sensibly the same at both 
temperatures. The right-hand members are nearly in proportion to the absolute 
temperatures. The pressure is measured in metres of mercury. Hence the 
volume of the gas, at 18° C. and one atmosphere, is (to the unit employed) 

2-6 + 2731/0-76 = 3596 nearly. 

Thus, by the above interpretation of Amagat's results, we have at 18° C. 

nirs* = 3-9/3596. 

Clerk-Maxwell, in his Bradford Lecture, \ ranks the various numerical 
data as to gases according to " the . completeness of our knowledge of them." 
The mean free path appears in the second rank only, the numbers in which are 
regarded as rough approximations. In the third rank we have two quantities 
involved in the expression for the mean free path, viz., the absolute diameter 
of a particle, and the number of particles per unit volume (s and n of the pre- 
ceding pages). 

To determine the values of s and n separately, a second condition is 
required. It has usually been assumed, for this purpose, that the volume of a 
gas, " when reduced to the liquid form, is not much greater than the combined 
volume of the molecules." Maxwell justifies this assumption by reference to 
the small compressibility of liquids. 

* Annates de Chunk, xxii. 1881. f Phil. Mar/., 1873, ii. 453. See also Nature, viii. 298. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 91 

But, if the above argument be, even in part, admitted, we are not led to 
any such conclusion, and we can obtain ns 3 (as above) as a quantity of the 
second rank. We have already seen that ns 2 is inversely proportional to the 
mean free path, and is thus also of the second rank. From these data Ave may 
considerably improve our approximations to the values of n and of s. 

Taking Maxwell's estimate of the mean free path in hydrogen, we have (to 
an inch as unit of length) 

5^ = 880.10- 8 . • 

From these values of ns 2 and ns 3 we have, approximately, for 0° C, and 1 
atmosphere, 

n = 16.10 20 , s = 6.10-\ 

The values usually given are 

n = 3.10 w , s = 2-3.1(T s . 

It must be recollected that the above estimate rests on two assumptions, 
neither of which is more than an approximation, (a) that the particles of 
hydrogen behave like hard spheres, (b) that they exert no mutual molecular 
forces. If there were molecular attraction the value of ns 3 would be greater 
than that assumed above, while ns 2 would be unaltered. Thus the particles 
would be larger and less numerous than the estimate shows. 

[Of course, after what has been said, it is easy to see that V should be 
diminished further by a quantity proportional to the surface of the containing 
vessel and to the radius of a sphere. But though this correction will become 
of constantly greater importance as the bulk occupied by a given quantity of 
gas is made smaller, it is probably too minute to be detected by experiment.] 



IX. Effect of External Potential. (Added June 15, 1886.) 

31. Another of Maxwell's most remarkable contributions to the Kinetic 
Theory consists in the Theorem that a vertical column of gas, when it is in 
equilibrium under gravity, has the same temperature throughout. He states, 
however, that an erroneous argument on the subject, when it occurred to him in 
1866, " nearly upset [his] belief in calculation."" 15 ' He has given various investiga- 
tions of the action of external forces on the distribution of colliding spheres, but 

* Nature, viii., May 29, 1873. Maxwell's name does not occur in the Index to this volume, though 
he has made at least five contributions to it, most of which hear on the present subject : — viz. at pp. 85, 
298, 361, 527, 537. 



92 PROFESSOR TAIT ON THE 

all of them are complex. The process of Boltzmann, alluded to in a foot-note 
to the introduction (ante, p. 66), and which Clerk-Maxwell ultimately pre- 
ferred to his own methods, involves a step of the following nature. 

An expression, analogous to the /of §3, but in which B and C are unde- 
termined functions of the coordinates x, y, z, of a point, is formed for the 
number of particles per unit volume, at that point, whose component speeds, 
parallel to the axes, lie between given narrow limits. I do not at present 
undertake to discuss the validity or the sufficient generality of the process by 
which this expression is obtained, though the same process is (substantially) 
adopted by Watson and others who have written on the subject. However 
obtained, the expression is correct. It can be established at once by reasoning 
such as that in §§ 2, 3, 4. To determine the forms of the aforesaid functions, 
however, a most peculiar method is adopted by Boltzmann and Maxwell. 
The number of the particles per unit volume at x, y, z whose corresponding 
" ends " occupy unit volume at u, v, iv in the velocity space-diagram (§ 3), is 
expressed in terms of these functions, and of u 2 + v 2 + w 2 . The variation of the 
logarithm of this number of particles is then taken, on the assumption that 

Sx = u8t, &c, 8u— St, &c, 

ax 

where U is the external potential; and it is equated to zero, because the 
number of particles is unchangeable. As this equation must hold good for all 
values of u, v, w, it furnishes sufficient conditions for the determination of B 
and C. The reasons for this remarkable procedure are not explained, but 
they seem to be as below. The particles are, as it were, followed in thought 
into the new positions which they would have reached, and the new speeds 
they would have acquired, in the interval St, had no two of them collided or had 
there been no others to collide with them. But this is not stated, much less 
justified, and I cannot regard the argument (in the form in which it is given) 
as other than an exceedingly dangerous one ; almost certain to mislead a 
student. 

What seems to underlie the whole, though it is not enunciated, is a postu- 
late of some such form as this : — 

When a system of colliding particles has reached its final state, we may assume 
that (on the average) for every particle which enters, and undergoes collision in, a 
thin layer, another goes out from the other side of the layer precisely as the first 
would have done had it escaped collision. 

32. If we make this assumption, which will probably be allowed, it is not 
difficult to obtain the results sought, without having recourse to a questionable 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 93 

process of variation. For this purpose we must calculate the changes which 
take place in the momentum, and in the number of particles, in a layer; or, 
rather, we must inquire into the nature of the processes which, by balancing- 
one another's effects, leave these quantities unchanged. 

Recur to § 29, and suppose the particles to be subject to a potential, U, 
which depends on x only. Then the whole momentum passing per unit of 
time perpendicularly across unit surface of any plane parallel to yz is 



J Vn Jr=Th> 



where n (the number of particles per cubic unit), and h (which involves the 
mean-square speed), are functions of x. 

At a parallel plane, distant a. from the first in the direction of x positive, 
the corresponding value is 

But the difference must be sufficient to neutralise, in the layer between these 
planes, the momentum which is due to the external potential, i.e., 



Hence 



dx 



1 p d n _ p d\J 

2 dxh dx 



or 



,d\J _ 1 dn 1 dh 
dx n dx h dx 



-2h^..=± -_— (1) . 



Again, the number of particles which, in unit of time, leave the plane unit 
towards the side x positive is 

- n I vv I cosPsinft dfi= — n / vV . 
2 <Jo >Jo 4 <so 

Hence those which leave the corresponding area at distance a are, in number, 

i( 1+a l)(^)- 

But, by our postulate of last section, they can also be numbered as 



where 



94 PROFESSOR TAIT ON THE 

This expression is obtained by noting that none of those leaving the first 
plane can pass the second plane unless they have 

*-C09-/3>2a Ta; - 

All of the integrals contained in these expressions are exact, and can therefore 
give no trouble. The two reckonings of the number of particles, when com- 
pared, give 

rfU 1 dn 1 dh 

dx ~n dx 2hdx ^ '' 

From (1) and (2) together we find, first 

— -o 

dx~ ' 

which is the condition of uniform temperature ; and again 

Avhich is the usual relation between density and potential. 

[In obtaining (2) above it was assumed that, with sufficient accuracy, 

To justify this : — note that in oxygen, at ordinary temperatures and under 
gravity, 

3 

^t = 1550 2 in foot-second units, 

™- 32 

dx " 

so that, even if a = 1 inch, we have approximately 

** ~. dx "300,000 J 

It is easy to see that exactly similar reasoning may be applied when U is a 
function of x, y, z ; so that we have, generally, 

where h is an absolute constant. And it is obvious that similar results may be 
obtained for each separate set of spheres in a mixture, with the additional 
proviso from Maxwell's Theorem (§§ 20, 21) that P/A has the same value in 
each of the sets. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 



95 



APPENDIX. 

The following little table has been calculated for the purposes of §§ 11, 28, 
by Mr J. Clark, Neil-Arnott Scholar in the University of Edinburgh, who used 
six-place logarithms : — 



X 


*i 


X 2 


XA 


x 3 


X 3/ X 2 


•1 


•000099 


•200665 


•00049 + 


•000990 


•00493 + 


•2 


•001537 


•405312 


•00379 + 


•007686 


•01896 + 


•3 


•007420 


•617838 


•01198 + 


•024676 


•03994- 


4 


•021814 


•841997 


•02591- 


•054537 


•06477 + 


•5 


•048675 


1-081321 


•04501 + 


•097350 


•09003- 


•6 


•090418 


1-339068 


•06752 + 


•150698 


•11254- 


•7 


•147091 


1-618194 


•09089 


•210130 


•12985 + 


•8 


•215978 


1-921318 


11241- 


•269973 


•14051 + 


■9 


•291870 


2-250723 


•12968 + 


•324301 


•14409- 


1-0 


•367879 


2-608351 


•14104- 


•367879 


•14104- 


11 


•436590 


2-995825 


•14572 + 


•396900 


•13249- 


1-2 


•491380 


3-414479 


14388 + 


•409409 


■11990 + 


1-8 


•527004 


3-865384 


■13633 + 


•405388 


•10488- 


14 


•541119 


4-349386 


•12441 + 


•386514 


•08887- 


1-5 


•533581 


4-867132 


•10962 + 


•355721 


•07309- 


1-6 


•506619 


5-419114 


•09348- 


•316637 


•05843- 


1-7 


•464174 


6-005696 


•07729- 


•273044 


•04546 + 


1-8 


•409127 


6-627149 


•06203 + 


•228404 


03447- 


1-9 


•352543 


7-283658 


■04840 - 


•185549 


•02547 + 


2-0 


•293040 


7-975359 


•03674 + 


•146520 


•01837 + 


21 


•236390 


8-702340 


•02715 + 


•112567 


■01294- 


2-2 


•185224 


9-464667 


•01956- 


084193 


•00889 


2-3 


•141065 


10-262360 


•01373 + 


•061333 


•00598- 


2-4 


•104541 


11-095474 


•00941 + 


•043559 


•00393- 


2-5 


•075390 


11-964016 


•00630 + 


•030156 


- -00252 + 


2-6 


•052962 


12-867980 


•00411- 


•020370 


•00158 + 


2-7 


•036242 


13-807388 


■00262 + 


•013423 


•00097 + 


2-8 


•024155 


14-782249 


•00162 + 


•008627 


00058 + 


29 


•015700 


15-792549 


•00099 + 


•005414 


•00034 + 


3-0 


009963 


16-838302 


•00057 + 


•003321 


•00019 + 



Here X^^g-* 2 and X s = xH~ x \ while X 2 = X£- x * + (2x 2 + l) 



•I- 



xi dx. 



The sum of the numbers in the fourth column is 1 '69268, so that the 
approximate value of the integral in § 11, which is 0'4 of this, is 0"67707. 

The sum of the numbers in the sixth column is 1*62601, so that the value 
of the integral in [the addition to] § 11 is about 0'6504. 



( S7 ) 



IV. — The Eggs and Larvce of Teleosteans. By J. T. Cunningham, B.A. 

(Plates I.-VII.) 

(Read 5th July 1886.) 

The purpose of this memoir is (1) to make known a number of drawings and 
descriptions of the eggs, embryos, and larvse of the species of Teleosteans which 
I have been able to study at the Scottish Marine Station ; (2) to review as 
comprehensively as possible what is known at the present time concerning the 
structure of the embryos and larvse of the species of Teleosteans, and to discover 
what features are common to each family or each order; (3) to discuss the changes 
which take place in the protoplasm and nucleus of the mature ovum immedi- 
ately after it is shed, both when fertilised and when unfertilised. The ova of 
the following species were taken directly from the parent fish, and artificially 
fertilised. The necessary operations were carried out, in some cases by myself, 
on board fishing boats — usually steam trawlers from Granton. In many 
instances I did not myself go out in the boats, but the ova were obtained and 
brought to me at the laboratory by Alexander Turbyne, keeper of the 
station. But in every case there is no uncertainty as to the species of the fish 
from which the ova were taken; if there was any doubt, specimens of the 
parent fish were brought with the ova. 

1. Clupea harengus, Linn. (Herring) (PI. I. figs. 1-3). 

The development of the herring has been described by Prof. C. Kupffer* 
in an elaborate memoir, which is illustrated by microscopic photographs. 
Among these, one figure of the hatched larva is given, but this is on too small 
a scale to exhibit the structure clearly. It is nearly two years since I studied 
the ova of the herring, and some of the drawings which I then made have been 
used to illustrate papers on particular problems in Teleostean development. t 
But, as far as I am aware, no good figures of the larva of the herring have been 
published, and I therefore think that the figures on PI. I. will not be super- 
fluous. Herring, as is well known, have two spawning seasons on the east 
coast of Britain — one in the spring, in February and March, and one in the 

* Ueber Laichen und Entwicklung des Ostsee-Herings, Berlin, 1878. 

t "On the Significance of Kupffer's Vesicle," &c, Quart. Jour. Micr. Sci., 1885; and "On 
Kelations of Yolk to Gastrula," &c, Ibid. 

VOL. XXXIII. PART I. N 



98 MR J. T. CUNNINGHAM ON THE 

autumn, in August and September. The eggs which I studied were obtained 
in August off the Longstone Lighthouse, Fearn Islands. 

Embryonic Period and Temperature. — Hatching took place on the eighth 
and ninth days, the temperature varying from 11°5 to 14° - 5 C. 

In the herring ovum the yolk consists of a number of nearly spherical 
translucent vitelline globules ; there are no oil globules. The blastodisc is 
large in proportion to the yolk. 

Diagnosis of Larva. — The length of the newly hatched larva is 5"2 to 53 mm., 
according to Kupffer. The mouth is open, the body is wholly transparent 
except the eyes, which are of a deep black, and perfectly opaque ; there are no 
red blood corpuscles; the notochord is unicolumnar ; the anus is at a distance 
from the yolk sac, being 1 mm. from the end of the tail; the pectoral fin is 
present as a simicircular fold of membrane ; the pelvic fin is not developed ; 
compact chromatophores are present on the sides of the body and tail. 

The larva? of the herring I have taken occasionally, but not often, in the tow- 
net. Two were obtained at 5 fathoms depth west of Inchkeith, Oct. 7, 1885 ; 
15 at a depth of 3 feet off St Abb's Head, Sept. 30, 1885 ; a few at 3 fathoms 
east of Inchkeith, May 14, 1885; and a few at 5 fathoms north-east of Inch- 
keith, April 15, 1885. 

2. Salmo levenensis (Loch Leven Trout) (PI. I. fig. 4). 

This figure is taken from an alevin of the species obtained from Sir James 
Maitland's hatchery at Howietoun. The larva was three days old ; the per- 
manent anterior dorsal, caudal, and anal fins have begun to develop, but the 
median larval fold is present behind the anterior dorsal, behind the anal, 
and between the anus and the yolk. The pelvic fins have appeared; they are 
situated some distance in front of the anus, and they have no connection with 
the preanal larval fin, which extends between them up to the yolk sac. 



3. Osmerus eperlanus, Lacdp (Smelt or Sperling) (PL I. figs. 5, 6). 

The mature egg of Osmerus, when first shed, is yellow in colour, and but 
slightly translucent ; it is surrounded by a double zona radiata, the inner 
surface of which is, as in all Teleosteans, in immediate contact with the vitellus. 
When the eggs are allowed to fall on to stones or glass plates in water contain- 
ing milt, they become attached and fertilised simultaneously. The attachment 
is effected in the following manner : — The outer zona radiata ruptures at the 
region of the ovum which is opposite the micropyle, and peals off the inner 
zona, becoming of course inverted in the process. Over a circular area sur- 
rounding the micropyle, the two layers of the zona remain firmly united. The 



EGGS AND LARVAE OF TELEOSTEANS. 99 

outer surface of the external layer or zona externa is adhesive, and the 
ruptured edge becomes attached, so that the ovum swings in the water from 
the flexible suspensory membrane thus formed. I have elsewhere * described 
the separation of the two layers of the zona resulting in the formation of the 
suspensory membrane, but the relation of the united parts of the two layers to 
the micropyle is now described for the first time, and is shown in fig. 6 as it 
appears in optical section. 

When fertilisation takes place, a large perivitelline space is formed by the 
elevation of the internal zona. Unfortunately, I was unable to obtain a sufficient 
number of healthy ova to study the development Fig. 5 was taken from an 
ovum fertilised at Stirling on May 6 ; it was drawn on May 7, twenty-five 
hours after the egg was shed. It shows the character of the egg, and the rela- 
tion of the blastodisc to the yolk ; but the blastodisc was not segmented, and 
it is possible that the ovum was not really fertilised, the formation of the 
blastodisc occurring normally in ripe Teleostean ova without fertilisation. The 
ovum resembles somewhat that of the herring. It is a little more transparent 
than the herring ovum, and the structure of the yolk is different. In the egg 
of Osmerus there are a number of oil globules, varying much in size, while the 
yolk of the herring ovum has no oil globules. The diameter of the fertilised 
ovum is 1*3 mm. 

4. Pleuronectes platessa, Linn. (Plaice) (PL II. figs. 1-3). 

The eggs of the plaice were artificially fertilised on board a steam trawler 
outside the Isle of May, February 3, 1886. The egg is 1*95 mm. in diameter, 
and like the other eggs of the Pleuronectidse which I have examined, has a 
perfectly homogeneous yolk. The perivitelline space is small. The larvae were 
not actually hatched, but one taken from the ovum, when almost ready to hatch, 
is shown in fig. 3. Its length is 4*1 mm. The eye is faintly pigmented. There 
are three rows of yellow dendritic pigment cells down each side, and black 
dendritic cells in the head. The anus is open, and situated immediately behind 
the yolk sac. The notochord is multicolumnar ; the pelvic fin not developed. 

5. Pleuronectes fiesus, Linn. (Common Flounder) (PI. II. figs. 4-8). 

Eggs of this species were obtained on March 30, 1886, in the Firth of 
Forth, in Aberlady Bay. It is the only species which has been found in 
abundance, and in the spawning condition, so far up the Firth. The egg is 
similar in all respects to that of the plaice except in size. It is 1 -03 mm. in 
diameter. The newly hatched larva is transparent, and 3*01 mm. in length. 

* Proc. Zool. Soc, London, 1886. 



100 MK J. T. CUNNINGHAM ON THE 

The anus is open ; notochord multicolumnar ;' ;: " small round pigment spots along 
the sides and head ; pelvic fin not developed. 

On March 5 of the current year I visited some fishing boats at Kincardine 
on the Forth. These boats were fishing with what are called bag-nets or stow- 
nets. A net of this kind is fashioned very much like a beam-trawl, and is 
fastened beneath the boat, so that its mouth faces the current of the tide ; the 
fish are thus washed into the net. Among the fish taken on the occasion of my 
visit were a large number of Pleuronectes Jlesus, which are commonly called 
fresh- water flounders, or mud flounders. Nearly all of these fish had a number 
of small round white tumours on the fins and on the upper or dark side. 
The tumours are cutaneous, and have been described more than once (see 
M'Intosh, Third Annual Report of Scottish Fishery Board). The fishermen 
stated that these tumours were the eggs of the fish, that the mud flounder 
carried its eggs on its back. On another occasion a bottle was sent to me from 
Elie, said to contain flounder spawn ; the contents when examined proved to 
be the greenish gelatinous egg-cases of some species of Chsetopod, perhaps 
Arenicola piscatorum, and within the cases were the trochospheres, whose green 
colour was the cause of the colour of the cases. 

5. Pleuronectes limanda, Linn. (Salt-water Flounder) (PI. II. figs. 9-11; 

PI. III. figs. 1-6). 

Ripe specimens of this species were obtained by me in considerable 
numbers on board a steam-trawler six or seven miles east-north-east of the Isle 
of May, on May 21 of the current year. A number of the eggs were squeezed 
out, artificially fertilised, and conveyed to the Marine Station. Living specimens 
were also successfully carried to the aquarium, and upon eggs taken from these 
I was able to study the condition of the ripe eggs immediately on their escape 
from the oviduct, and the earliest processes of fertilisation and development. 

The egg, after the formation of the perivitelline space, is '84 mm. in diameter; 
the appearance, magnified 33 times at the close of simple segmentation, is 
shown in PI. II. fig. 9. 

Hatching took place on the third day; the temperature of the surface of 
the sea where the eggs were taken was 7° 5 C, and the temperature of the water 
containing the eggs varied from this to 10° C. 

The newly hatched larva was 2*66 mm. in length ; the structure closely 
similar to that of other species of the genus; notochord multicolumnar ; mouth 
not open; small black pigment spots on sides of the body; anus close to the 
yolk, and not open. 

* The terms unicolumnar and multicolumnar applied to the notochord refer to the arrangement of 
the vacuoles, which are very conspicuous in newly hatched fish : in the herring and a few other cases 
these vacuoles arc cubical, and form a single linear series ; in other cases there are several series. 



EGGS AND LARV^ OF TELEOSTEANS. 101 

The figures given of the first processes of fertilisation and development will 
be considered in a subsequent section. 

On Dec. 5, 1885, 1 trawled with a fine meshed shrimp trawl across the Drum 
Sands, which are situated between Queensferry Point and Cramond Island, 
and obtained a considerable number of young Pleuronectes limanda. These 
were about 2 inches long, and could be identified from the semicircular curve 
in the lateral line above the pectoral fin. Larger, nearly full-grown, specimens 
were also taken, and kept for some time in the aquarium, where they lived 
healthily. 

In June of the current year, Mr Ramage, who is at present studying at the 
station, pointed out to me that the sands to the west of the laboratory were 
swarming with young flounders. These were about £ inch long, and had 
already reached the condition of the adult ; they showed no trace of larval 
structures. But I was unable to identify these young fish, as the lateral line 
could not be clearly distinguished. It is of course probable that the young of 
many different species are present in such situations in the summer months. 
It is pretty certain that nearly all our valuable flat-fishes pass the early post- 
larval stages of their existence on littoral sand-flats. Mr Geokge Brook 
informs me that large numbers of young flat-fish are destroyed by shrimpers 
in such situations. With regard to this particular locality, I have never seen 
any shrimping carried on in the neighbourhood. 

6. Pleuronectes cynoglossus, Linn. (Witch) (PI. III. figs. 7-9 ; PI. IV., PI. V.). 

Of the developing eggs of this species I made a particularly careful study, 
with. the intention of obtaining, if possible, greater certainty on the various 
points in dispute concerning the earliest changes that the mature ovum under- 
goes after being shed. A number of living specimens of the fish were trawled 
by the " Medusa," on 23rd and 24th June of the current year, at a place called 
Fairlie Patch, opposite the town of Fairlie, in the channel between the island 
of Cumbrae and the mainland. The fish were taken alive to the little labora- 
tory known as the " Ark," which was originally a floating structure, but is now 
firmly established on the beach at the east side of Millport Bay. I have given 
a large number of figures, illustrating the successive stages in the development 
of this species. After the formation of the perivitelline space they are 1*155 
mm. in diameter. The yolk is perfectly transparent, but the zona radiata is 
thicker than in most of the other species of the genus. The perivitelline space 
is very small. During the time the eggs were under observation the weather 
was very fine, and the laboratory being fully exposed to the sunshine, became 
in the middle of the day very hot. I had no means of regulating the tempera- 
ture of the water containing the eggs, and on two occasions it rose to 20° "5 C. 



102 MR J. T. CUNNINGHAM ON THE 

This temperature was fatal to a large number of the developing eggs. The 
temperature of the water in which the eggs were first placed was 12°5 C. With 
these great variations in temperature, hatching took place on the sixth day. 
The larva is not different from that of the other species of Pleuronectes ; its 
length is 3*9 mm.; there is no pigment in the eye ; a number of very minute 
pigment spots are scattered down the sides. The anus is not open, and the 
coalesced segmental ducts do not communicate with the rectum (see PL V. fig. 5). 
PL V. fig. 7, shows the condition of the larva a little more than forty-eight 
hours after hatching. The length is now increased to 5 9 mm. — a very rapid 
rate of growth. The median fin-fold is much wider. The eye is slightly 
pigmented, and pigment is largely developed in the skin of the body. The 
cutaneous chromatophores form five well-marked transverse stripes, arranged 
in longitudinal series along the sides, three of them on the tail, one in the 
region of the rectum, and one about the pectoral fin. No trace of the pelvic 
fin is to 'be seen. The operculum is present as a slight fold, and beneath it 
the first branchial cleft is widely open; behind this are four clefts indicated but 
not perforated. The mouth is also still wanting. 

7. Pleuronectes microcephalics (Lemon Sole). 

I have not obtained fertilised ova of this species, but I was able to ascertain 
from examination of unfertilised mature examples that there are no oil globules, 
and that the diameter measures 1*1 mm. The ripe females, from which the 
mature eggs came, were taken in the trawl east of May Island, May 22 of the 
current year. 

8. Gadus wglefinus, Linn. (Haddock) (PL VI. fig. 1). 

The ova of Gadus morrhua, G. wglefinus, and G. merlangus, in various 
stages of development, have been previously figured by me.'" The larvae, after 
hatching, were not described in the paper I refer to. The newly hatched cod 
has been correctly figured by John EYDER.t For the sake of comparison, I 
give a figure of the newly hatched larva of the haddock. The eye is pigmented, 
and there is a single row of dendritic chromatophores along each side ven- 
trally. The anus is not open, nor the mouth ; the pelvic fin is also wanting. 
In all respects, except in size, the larva of the haddock resembles that of 
the cod. 

The following species of ova and larvae were not obtained directly from the 
parent fish, but identified from other considerations. 

"Relations of Yolk to Gastrula in Teleosteans," Quart. Jour. Mia: Sci., 1885. 
t Report of American Fish Commission for 1882, Washington, 1884. 



EGGS AND LARVAE OF TELEOSTEANS. 103 

9. Cottus scorpius, Linn. (PL VI. fig. 2). 

The eggs ascribed to this species were brought in to the station on February 
14 of the present year. They formed large masses of dark red colour, and 
were attached to the rocks between tide marks. The ova are but slightly 
translucent ; the zona radiata is. thick. The figure shows the appearance under 
a low power of the microscope. The yolk is homogeneous, except for the 
presence of scattered oil globules, irregular in number and size, and contains 
the pigment, which, yellowish-red as seen in each separate ovum, gives the 
whole mass a darker red colour. The diameter of the vitelline membrane is 
203 mm., of the ovum 1*81. The identification is founded on some remarks of 
Professor M'Intosh, who observed the deposition of similar eggs in the 
aquarium of the Marine Laboratory at St Andrews (see Third Annual Report 
Scottish Fishery Board, 1885, App. F.). 

Agassiz # has stated that the eggs of Cottus groenlandicus, which is only a 
variety of Cottus scorpius, are pelagic. His conclusion rests apparently on the 
identification of the oldest stage of larvae from a certain kind of pelagic eggs 
with the adult Cottus, and this mode of identification is of course not abso- 
lutely certain. 

10. Liparis Montagui, Cuv. (PI. VI. figs. 3, 4). 

Small masses of adhesive eggs are frequently obtained attached to tufts of 
Hydrallmannia falcata, Hincks. I have obtained such specimens in the months 
of May and June, both from long lines laid outside the Isle of May and from 
the dredge in the upper parts of the Firth. By the fishermen the eggs in 
question are usually believed to come from the herring or the haddock, and 
even naturalists of some experience have confounded them with herring spawn, 
which also often adheres to specimens of Hydrallmannia. The mass from 
which fig. 3 was taken was attached to a piece of Hydrallmannia left by the 
tide on the beach near Cramond Island, and was obtained May 7, 1886. The 
longest diameter of the egg, including the vitelline membrane (zona radiata) 
was 1*27 mm., the transverse diameter of the yolk sac '87 mm. The zona 
radiata is of considerable thickness, and shows a division into two layers. The 
yolk is homogeneous and transparent, and contains three or more oil globules of 
various sizes. The mass of eggs seen with the unaided eye was colourless and 
transparent. I have identified the ova as those of Liparis Montagui, from some 
remarks of Prof. MTntosh in Keport on the St Andrews Laboratory, in the 
Third Annual Report of the Scottish Fishery Board, but the identification is 

* Proc. Amer. Acad. Arts and Scl, vol. xvii. ; and Memoirs of Mus. Comp. Zool., Harvard, vol. xiv. 
No. 1, pt. i. 



104 MR J. T. CUNNINGHAM ON THE 

not certain. M'Intosh says that the eggs of Lijiaris Montagui are found in 
shallow water, attached to such zoophytes as Hydrallmannia and Sertularia, and 
also to red Algae, and are of a pale straw colour. The eggs I have described 
were well advanced in development, so that the colour may have been present 
at an earlier stage, the colour of such eggs often disappearing as develop- 
ment proceeds. The eyes were considerably pigmented. 

Fig. 4 is a sketch of a fish hatched from some eggs exactly similar to those 
above described, which were taken in the trawl between Inchkeith and Burnt- 
island, April 29, 1884. The age of the young fish was two days after hatching. 
The eyes are deeply pigmented, the mouth completely developed, the pectoral 
fin is large, and covered with black pigment spots, and there is a row of similar 
spots along the ventral edge of the tail on each side. A small remnant of the 
yolk is still present, containing a single oil-globule. 

11. Cyclopterus lumpus, Linn. (Lump-sucker) (PL VI. fig. 5). 

To amateur naturalists on the coasts of Scotland the large masses of yellow- 
ish spawn of this fish, watched by the male parent, the " rawn and cock paidle," 
as they are called in the Scotch dialect, are a not unfamiliar sight. I regret to 
say I have not had an opportunity of personally observing the phenomenon in 
its natural state. But masses of the ova of Cyclopterus have been frequently 
brought into the station by boys; they are found attached to the rocks near the 
station, not far from low water mark. The colour of the eggs varies from red 
to pale yellow or nearly white. The yolk contains numerous oil globules of 
various sizes, arranged in a cluster at the ventral pole, but is otherwise homo- 
geneous. The perivitelline space is small. The eggs are but slightly trans- 
lucent. The diameter is 2 60 mm., inclusive of the vitelline membrane. The 
young Cyclopterus, when first hatched, is 4 mm. in length, but not so far 
advanced in development as the stage figured by Agassiz * of the same length. 
The anus is immediately behind the yolk sac, which forms such a contrast 
in size to the tail that the fish is tadpole-like in form. The body is quite 
opaque, and the blood red. The eyes are completely pigmented. The 
embryonic fin fold persists extending forwards dorsally a little beyond the anal 
region, but fin rays have appeared in the membrane. Both paired fins are 
well developed, the ventrals forming a median sucker, which differs only from 
that of the adult in exhibiting the fin rays in a more primitive condition. The 
skin contains numerous regularly distributed chromatophores. 

The young Cyclopterus, both immediately after hatching and in later stages, 
occur very plentifully among the Algae on the shore at Granton, and everywhere 
on the British coasts. They are also frequently taken in the tow-net at a 

* Young Stages, iii. 



EGGS AND LARV^ OF TELEOSTEANS. 105 

distance from the shore, but in this case are usually attached by the sucker to 
floating pieces of sea-weed. The eggs are deposited in January and February, 
and the young stages are to be found on the shore or in the tow-net through- 
out the summer. It was observed by Mr Jackson, in the Southport Aquarium, 
that the male parent, watching over the eggs, kept up a continual motion of his 
pectoral fins in close proximity to the eggs, and it appears that this is neces- 
sary to secure the sufficient oxygenation of the eggs, which are laid in such 
large masses that the central ones might easily in still water be asphyxiated. 
Young specimens of Cyclopterus were taken in the tow-net in the following 
localities : — Surface, 30 miles north-east of May Island, July 17, 1885 ; surface, 
near Inch Mickery, Aug. 26, 1885 ; surface, Firth of Forth, two occasions, 1884; 
surface, east of Craig Waugh, May 1884. I have never taken any large 
numbers either of these or any other fish larvae in the tow-nets. 

Species not identified. 

A certain number of well-marked species have been obtained by tow-net 
collecting, which I have not yet been able to identify. There are two possible 
methods of identifying an unknown species of pelagic ovum. One is to 
compare it, or the larva hatched from it, with figures and descriptions of ova or 
larvae already known; the other, to keep a number of specimens of the ovum 
in question alive until they hatch, and then to keep the larvae till they attain 
the specific characters of the adult fish. Both of these methods are liable to 
error. 

Species No. 12 (PI. VII. fig. 2). 

This form is easily distinguished by one conspicuous characteristic, namely, 
that the perivitelline space is very wide. The yolk is perfectly homogeneous 
and transparent. The diameter of the vitelline membrane is 21 mm., of the 
ovum 1 *2 mm. The eggs were obtained in the latter end of March, both in 
1885 and 1886, about 10 miles east of the Isle of May. Unfortunately, time 
could not be found to give sufficient attention to the form to isolate it and 
keep it alive till hatching took place. Thus the characters of the larva were 
not ascertained, and no egg at all similar has been taken directly from an 
adult fish. 

Species No. 13 (PI. VII. figs. 3, 4). 

The eggs of this species were obtained in the tow-net, 16 miles beyond 
the Isle of May, on April 30, and off Gullane Ness, May 27, 1886. The 
diameter of the ovum, including the vitelline membrane, is "84 mm. The peri- 
vitelline space is small; there is a single oil globule situated beneath the 

VOL. XXXIII. PART I. O 



106 MR J. T. CUNNINGHAM ON THE 

posterior end of the embryo. Some of the eggs were hatched, and fig. 4 shows 
the form of the larva immediately after hatching ; the length is 21 mm. ; the 
notochord, as seen in fig. 4a, is mnlticolnmnar ; there are black pigment spots 
on the body, but the eye is unpigmented ; the pigment on the post-vitelline 
part of the body forms two black transverse bands. The intestine was, I believe, 
not open, but a solid extension of it extended to the ventral edge of the larval fin. 

In a great many respects the present species agrees with Motella mustela, 
Linn., as described by George Brook,* from eggs actually observed to be 
deposited by the parent. There are several minute points of difference. 
Brook's measurement of the ovum is '655 to - 731 mm. in largest diameter, 
while he gives the length of the newly hatched larva as 2 - 25 mm. ; thus the 
diameter of the ovum given by Brook is slightly less than my measurement, 
while the length of the larva given by him is slightly greater than what I have 
stated. The position of the oil globule and rectum is also different in my 
figure from that in Brook's. But the points of agreement are more numerous 
and important than the points of difference ; the arrangement of the pigment, 
for instance, is exactly the same in the two accounts. It is evident, therefore, 
that the species I have described is either Motella mustela, Linn., or some other 
of the four British species of Motella. 

Pelagic eggs closely similar to the species here described, and to those of 
Motella mustela as described by Brook, have been described by A. Agassiz and 
C. O. Whitman^ and referred with some uncertainty to Motella argentca, 
Rhein. Two other species of pelagic eggs have also been provisionally ascribed 
by those authors to the genus Motella. 

Species No. 14 (PI. VII. figs. 5, 6). 

This form is well characterised ; it possesses one feature which, as far as 
extant observations show, is present in no other pelagic ovum, namely, that the 
yolk is divided into a number of polyhedral masses. This egg is the most 
perfectly pellucid of all I have observed, and the planes of division in the yolk 
appear in optical section as extremely fine lines. The egg is slightly oval in 
shape, '94 mm. by -97 mm. in diameter. The newly hatched larva is 363 mm. 
in length, the notochord is unicolumnar, and the anus is separated from the 
yolk by two-thirds of the length of the post-vitelline part of the body, as in the 
herring ; the larva is absolutely without pigment. The eggs were obtained in 
1884 and 1886, in the latter end of May and during June. In each season 
they were taken within the Firth of Forth, between Gullane Ness and 
tin; island of Inchkcith. This form, from its conspicuous characteristics, has 

* Linn. Soc. Jour., vol. xviii. 

t '' Pelagic Stages of Young Fishes," Memoirs of Mas. Comp. Zool. Harv., vol. xiv., No. 1. 



EGGS AND LARVAE OF TELEOSTEANS. 107 

long been known, but all attempts to trace it with certainty into connection 
with a particular species of fish have hitherto failed. The eggs and larvae 
were first described by A. Agassiz* in 1882, under the name Osmerus mordax, 
Gill, figures being given of the newly hatched larva and some older stages. 
Agassiz appears to have obtained his figures of the later stages from specimens 
taken in the tow-net, not from larvae reared in captivity directly from the egg. 
He states that at first he supposed the larvae to belong to some Clupeoid species, 
until he saw a paper by Mr H. J. Eice, on the development of Osmerus, when 
he became convinced that his specimens were really to be ascribed to Osmerus 
mordax. He points out that the oldest larva he figures has a striking 
resemblance to Scombresox and Belone. As a matter of fact this resemblance is 
not very exact, and as it is known that the eggs of all the Scombresocidw are 
provided with filamentous processes of the vitelline membrane, it is certain that 
the ovum under consideration cannot belong to any member, of that family. 
Agassiz also remarks that the resemblance of the development of Osmerus to 
that of the herring as given by Sundevall t is very close. Now Sundevall 
gives a figure of the larva of Osmerus eperlanus, which shows an oil globule in 
the yolk sac, and I have shown that the ovum of O. eperlanus is adhesive. Thus 
it is impossible that Agassiz' larva should be that of Osmerus mordax. Two 
species of the same genus could not differ so greatly in the structure of their 
ova and the conditions to which those ova are exposed, as do the pelagic ovum 
we have been considering, and the ovum of Osmerus eperlanus. Moreover, 
Osmerus mordax does not occur in the British seas. It is certain that the 
herring cannot be the parent of the ovum in question, in spite of the resem- 
blance between the larva derived from it and the herring larva, for the ova of 
the herring are well known, and are not pelagic. This same pelagic ovum and 
larva have been described by V. Hensen,J and that gentleman, courteously 
replying to inquiries of mine on the subject, said, in his opinion, the parent 
species was the sprat. But here we have the same difficulty as in the case of 
Osmerus. Can any species of Clupea have pelagic ova? No instance is yet 
known of a typically adhesive and a typically pelagic ovum occurring in the 
same genus. Nevertheless the segregation of the yolk in our pelagic ovum is 
not altogether incomparable with the condition of the yolk in the herring. It 
seems absolutely certain that the problematic ovum belongs to some physosto- 
mous fish, but hitherto no physostomous fish is known to have a pelagic ovum. 
It has struck me as possible that the parent we are seeking to discover is really 
the eel, Anguilla vulgaris. At all events the fertilised spawn of the eel has 
never been examined. 

* Young Stages, pt. iii. f Svensk. Vetensk. Akad., 1855. 

% Vierter Ber. Com. Unt. Deutsches Meere, Berlin, 1883. 



108 MR J. T. CUNNINGHAM ON THE 

Species No. 15, PI. VII. fig. 7. 

These ova formed a cylindrical rope-like mass, and were brought up on a 
tow-net line from a depth of about 30 fathoms in the Gulf of Guinea. They 
were obtained by Mr John Rattray, on two occasions when he was on board 
the steamer " Buccaneer," a telegraph steamer placed at the disposal of Mr 
J. Y. Buchanan, for hydrographical investigations. The first occasion was on 
March 12 of the current year, in lat. 1° 17' N., long. 13° 56'6' W. ; the second 
occasion was soon after, not far from the same locality. The depth of the 
ocean at the place was 2725 fathoms. The felted filaments in the rope-like 
mass were internal, the eggs external. Each ovum was 1 5 to 1 '6 mm. in diameter. 
They are, as far as I am aware, the first Teleostean ova which have been found 
to have a group of filamentous processes at each of two opposite poles of the 
vitelline membrane. In these ova one group of processes is rudimentary and 
functionless, but nevertheless the system of processes is closely similar to that 
which occurs in Myxine (see my paper on " Reproductive Elements of Myxine 
glutinosa," Quart. Jour. Micr. Set., 1886). Gobiidse, Blenniidae, Pomacentridse, 
Atherinidge, Scombresocidse are the only families known in which processes of 
the vitelline membrane occur, but it is impossible to say which of these families, 
if any, includes the parent of the ova described. 

Identification of Ova. — The identification of the numerous pelagic ova which 
are taken in the tow-net at the mouth of the Firth, at different times of the 
year, cannot at present be carried out with complete certainty. If the eggs and 
larvae of every species known to occur were adequately described and figured, 
the feat might be possible ; but at present the identification of any egg taken 
from the sea must always be subject to a certain degree of scepticism. I 
have several times attempted to assign the eggs in a tow-net gathering each 
to its parent species, and have satisfied myself that I had separated the 
eggs of the Plaice, Cod, Haddock, PI. fiesus, and Trigla gurnardus. But 
there may be other species with closer resemblances to these than I am at 
present aware of. 

General Comparative Review of the Structure of the Ova and Larva? 

of Teleosteans* 

The method followed in the present section is to take the families of each 
Order successively, and inquire what is known concerning the characters of 

* The classification employed in the present section is— 
I. Physostonii. 
II. Physoclisti. 

1. Anacanthini. 2. Acanthopterygii. 3. Acanthopt. Pharyngognathi. 

i. Lophohranchii. 5. Plectognathi. 



EGGS AND LARY^ OF TELEOSTEANS. 109 

the eggs and larvse, then to ascertain what features are common to all the 
families of the order, and finally to compare the characters which belong to the 
several orders. We shall take the families as denned by Gunther in the 
article " Ichthyology" of the Encyclopaedia Britannica. 

Fam. 1. SiluriDjE. 

The female of Aspredo batrachus attaches the eggs to the skin of her own 
ventral surface, and carries them about there until they are hatched. The 
male Arius carries the eggs about in his pharynx. The male Callichthys 
makes a nest. 

An account of the breeding and development of Amiurus albidus (Lesueur), 
Gill, is given by John A. Ryder in Bull. U.S. Fish. Com., vol. iii. The ovum 
is adhesive, and ^ inch in diameter after fertilisation ; the vitellus was \ inch 
in diameter. The female deposited the whole of her eggs at one time in a 
tank, in one mass, which was 6 inches in length by 4 in width, by § inch in 
thickness. The male watched over the mass with great assiduity till hatching- 
occurred, and constantly fanned the eggs with his anal, ventral, and pectoral 
fins. The perivitelline space in the develoj>ing ovum was crowded with free 
refringent corpuscles, a fact not noted in any other Teleostean ovum. Hatch- 
ing took place on sixth to eighth day. The intestine in the larva ends not very 
far behind the yolk sac. 

Fam. 2. Scopelid^e. 
„ 3. Cyprinid^e. 

The carps are all fresh-water fishes. The eggs are in most cases adhesive, 
and attached to aquatic plants. The zona radiata is double. Carassius 
auratus, L., the gold-fish, and the variety known as the telescope-fish, 
attach their eggs to water plants (M. von. Kowaleswki, Zeit. f. iviss. Zool., 
Bd. xliii.). 

The larvae of Cyprinus (Leuciscus) rutilus and C. idus are figured by 
Sundevall. These figures are curious. In the newly hatched larva they show 
the yolk apparently extending back to the anus ; that is to say, although the 
anus is near the end of the tail, as in other physostomous larvse, the yolk, 
instead of being ellipsoidal in shape, is elongated, and occupies, in addition to 
its usual space, the interval ordinarily taken up by the preanal median fin-fold. 
The latter structure is shown in a normal state of development in stages sub- 
sequent to the absorption of the yolk, and it is possible that the apparent 
anomaly in the earlier stages is due to want of definition in the drawings, as 
in Sundev all's figures generally the limit between intestine and yolk sac is 



110 ME J. T. CUNNINGHAM ON THE 

not clearly shown. The eggs were hatched in May. The newly hatched larva 
of Leuriscns rutilus is 6*5 mm. long, of L. idus, 73 mm. 



Fam. 4. Kneriid^e. 

„ 5. CHARACINIDiE. 

„ 6. CYPRINODONTIDiE. 

Many of the Cyprinodonts are viviparous. The males are always much 
smaller than the females. A. Agassiz has figured some late stages of one 
species, Fundulus nigrofasciatus, C. and V., but his youngest stage has the 
homocercal tail already complete, and does not allow one to judge of the 
characters of the newly hatched larva. 

Fam. 7. Heteropygii. 
„ 8. Umbrid^e. 
„ 9. scombresocidjl 

The position of this family is somewhat doubtful; it is placed by Gunther 
among the Physostomi, although the air-bladder has no duct. By Claus 
(Grundzuge der Zoologie, 4th ed., 1882), the family is added to the Anacanthini. 
The peculiarities of the vitelline membrane in this family were first noticed and 
described by Haeckel (Muller's Archiv, 1855). Prof. Kolliker, in the Verh. d. 
Pln/sik u. Med. Ges. zu Wurzburg, 1858, corrected and added to Haeckel's 
observations. A clear and satisfactory description of the membrane, with its 
filamentous processes, is given by John A. Ryder, in his paper on the Develop- 
ment oi Belone longirostris = Belone truncata, Gunther (Lesueur) (Bull. U. S. Fish 
Commission, vol. i. 1881). From that paper we learn that the egg of Belone 
is much heavier than sea water, and sinks rapidly to the bottom when un- 
disturbed ; and also, that by means of the filaments, large numbers of the eggs 
spawned from the same female are fastened together, and the clusters usually 
become attached to foreign objects in the water, which objects may of course 
chance to be either fixed or in a state of free suspension. The vitellus is 
optically homogeneous, and the whole egg transparent, though, I infer, less so 
than pelagic ova, The larva, after hatching, is not figured, but as far as can be 
judged from figures of the embryo within the vitelline membrane, the anus is 
in immediate proximity to the yolk. This point cannot be definitely decided. 
The egg of Belone truncata is rather large, measuring, according to Ryder, 
I inch diameter, or, as measured from the figure given by him, 3*49 mm. 

The vitelline membrane is provided with filaments similar to those of 
Belone in the genera Scombresox, Hemirhamphus, and Exocoetus (flying fish). 
Arrhamphus' eggs have not been examined. The eggs of Belone vulgaris, 



EGGS AKD LARVAE OF TELEOSTEANS. Ill 

Fleming, have been examined by Mr Francis Day, and a short description 
of the filaments is given in his British Fishes. The species occurs on the 
British coasts. It is not uncommon on the south coast, and, according to 
Parnell, enters the Firth of Forth in July. I have not obtained any 
specimens hitherto. 

It is worthy of note, that if I am right in judging from Ryder's figure that 
the rectum in the larva of Belone is in contact with the yolk sac, this fact 
confirms the view of Claus, that the Scombresocidse do not belong to the 
Physostomi. 

Fam. 10. Esocid,e. 

There is only one genus in this family, Esox, the pike. The eggs of Esox 
Indus, Linn., have frequently formed the subject of embryological investigation, 
and were part of the material on which was based the classical memoir of 
Lereboullet, " Recherches d'Embryologie Comparee sur le Brochet, l'Ecrevisse 
et la Perche " (Ann. d. Sci. Nat., ser. iv. vol, i. 1854). 

The eggs are small, and are deposited in February and March. They are 
adhesive and attached to aquatic plants in narrow creeks or ditches (Day). 

The larvae of the pike at different stages are described and figured by 
Sundevall (Svenska Vet. A/cad. Hand., 1855). The youngest stage figured is 
two days old. The anus is nearer to the end of the tail than to the yolk sac ; 
the pectorals are developed, but not the ventrals ; the eye is considerably pig- 
mented, and chromatophores are scattered all over the body ; the length is 10 
mm. ; the newly hatched larva is 9 mm. long. It is noteworthy that the pelvic 
fins have no relation in development to the ventral fin-fold ; the latter persists, 
extending between the pelvic fins and in front of them long after they have 
begun to appear. 

Fam. 11. Galaxiid^e. 
„ 12. Mormyrid^. 
„ 13. Sternoptychid^e. 

Argyropelecus hemigymnus, Cocco, was dredged between the Shetland and 
Faroe Islands by the "Porcupine" in 1869. Most of the species are pelagic, 
some abyssal. The eggs are large (Day, Brit. Fishes). 

Fam. 14. Stomiatid^e. 

,, 15. SALMONID.E. 

The ova of Salmo are large, heavy, and non-adhesive. In the newly 
hatched larva of this genus, or alevin as it is commonly called, the anus is at 



112 MR J. T. CUNNINGHAM ON THE 

a distance from the yolk, a preanal embryonic fin separating the two, as in the 
herring. The notochord, however, is multicolumnar. As has already been 
mentioned in the case of Esox, the preanal fin-fold extends between and in 
front of the pelvic fins in the alevin of Salmo. 

The larva of Coregonus oxyrhynchus, Nilss., at different stages is figured by 
Sundevall (loc. cit.). The ova were deposited from 6th to 10th November, and 
hatched in the following February ; they fall loose and separate to the bottom 
of the water ; the diameter measures 3 mm. The newly hatched embryo is 
11 mm. long; the anus is near the end of the tail, far removed from the yolk 
sac. The jtelvic fins develop at the sides of the preanal fin long before the 
latter disappears, and the position of the pelvic fins is behind the anterior end 
of the preanal fin, where it meets the yolk-sac. 

The ova of Thymallus (Grayling) are similar to those of Salmo, but smaller. 
The ova of Osmerus {eperlanus at all events) are adhesive, the external adhesive 
layer of the zona radiata peeling off from the inner, and forming a suspensory 
membrane. Sundevall (Svensk. Akad., 1855) gives figures and description of 
the newly hatched larva of Osmerus eperlanus; its length is 5 5 mm., the anus 
is near the end of the tail, there is a single oil globule in the yolk, the eye is 
slightly pigmented ; the eggs were obtained May 2, hatched May 20, 1855. 
Agassiz and Whitman {Pelagic Stages, p. 38) remark that the development of 
the pelagic egg they believe to be Osmerus mordax closely resembles that of 
the herring as given by Sundevall. They seem to have overlooked Sunde- 
vall's figures of Osmerus. The presence of an oil-globule in the larva of the 
latter genus is sufficient to prevent its being confounded with the larvasup- 
posed by the American authors to belong to Osmerus mordax. 



Fam. 16. Percopsid^e. 
„ 17. Haplochitonhle. 
„ 18. gonorhynchid^. 
19. Hyodontid^e. 



Fam. 20. Pantodontid^e. 

21. osteoglosshle. 

22. Clupeid^e. 



The ova of Clupea harengus, Linn., have been carefully studied. The ova 
are heavy and adhesive. The yolk is composed of a number of spherical or 
nearly spherical yolk spheres, with no oil-globules. The blastodisc is large, 
forming about one-fifth of the whole egg. The newly-hatched larva is pelagic 
and very transparent, the anus is far behind the yolk sac, the notochord 
unicolumnar, the eyes slightly pigmented, but no pigment in the rest of 
the body. The fertilised eggs and larva? of Clupea sprattus, Linn., have never 
been observed. Eggs, apparently mature, were pressed by Mr Duncan 
M vithews from a few specimens of the fish which had well-developed ovaries. 



EGGS AND LAHV^ OF TELEOSTEANS. 113 

The ova were apparently adhesive, similar to those of the herring, but 
considerably smaller (Report on the Sprat Fishing of 1883-84, Second Annual 
Report of the Scottish Fishery Board, 1884). 

The eggs of Alosa sapidissima have received much attention from the 
United States Fish Commission, They differ from those of the herring in not 
being adhesive ; they are deposited in fresh or brackish water, and are but 
slightly heavier than the water itself, so that they remain in a state of 
suspension near the bottom. It is a curious fact that, although the artificial 
cultivation of shad ova has been practised on such a large scale in America, no 
memoir on the development of the fish has appeared in the publications of the 
U. S. Commission. I have not been able to find any figure of the ova at any 
stage of development, but Mr John A. Ryder, in a paper on the absorption of 
the yolk in embryo fishes [Bulletin U. S. Fish Commission, vol. ii., 1882), gives 
a figure of the anterior region of a larval Alosa, some days after hatching. All 
that can be drawn from this figure is that the notochord is multicolumnar. 



Fam. 23. Bathythrissid^e. 

„ 24. CHIROCENTRIDiE. 

„ 25. Alepocephalidve. 

s , 26. NOTOPTERID^E. 

„ 27. Halosaurid^e. 



Fam. 28. Hoplopleurid^e. 
„ 29. Gymnotid^e. 
„ 30. Symbranchid^e. 
31. Muraenid^e. 



A great deal has been written about the reproductive organs of Anguilla 
and Conger. The fertilised ova have never been seen, but young eels about 2^ 
inches long are common enough in canals and rivers in spring. Specimens 
from the Forth and Clyde Canal were brought to me in April 1886. For an 
account of the investigations which have been made into the reproduction of 
the eel, see G. Brown Goode, Bull. U. S. Fish. Commission, vol. i., 1881. 

From the above survey it is seen that no physostomous fish is known at 
present to have pelagic ova. In the newly-hatched larvae, at present known, 
the anus is separated by a considerable interval from the yolk sac. In the 
Clupeidse the notochord is unicolumnar, but this is not a feature common to the 
order, as that organ is multicolumnar in the newly-hatched Salmo. It seems 
pretty certain that the problematic ovum, which Agassiz and Whitman 
identified as belonging to Osmerus mordax, is derived from some physostomous 
fish. V. Hensen suggested, in a letter to me, that it was the ovum of the sprat, 
but without evidence this is improbable, and it is not supported by the account 
of the sprat's ovum given by Duncan Matthews. As no one has seen the 
embryo of the eel, it possibly belongs to Anguilla, but in that case one would 
expect to find the ova more plentiful. 

VOL. XXXIII. PART i. p 



114 MR J. T. CUNNINGHAM ON THE 

Order II. ANACANTHINI. 
Fam. 1. LYCODiDiE. 

I am not aware that the development of any species of this family has been 
studied. 

Fam. 2. GADiDiE. 

Gad us. — A large number of the species of this genus have been studied— 
Gadus morrhua, merlangus, and wglefinus by myself, G. morrhua by John A. 
Ryder. The eggs are, of course, closely similar except in size. The largest of 
the three species above mentioned are those of G. ceglefinus. The eggs are 
pelagic, the yolk is optically homogeneous, and destitute of oil globules. In the 
newly hatched larva the anus is not open, the rectum is in immediate proximity 
to the yolk sac, the notochord is multicolumnar, the pelvic fins not developed, 
and the mouth not open. In the neAvly-hatched haddock the eyes are 
considerably pigmented ; there are stellate chromatophores scattered over the 
sides of the trunk, and a single row of them along the ventral edge of each 
side of the tail. 

Motella. — The development of Motella mustela, Linn., the five-bearded 
rockling, has been studied by George Brook {Jour. Linn. Soc, 1884, vol. xviii.). 
The eggs were deposited in his aquarium, under observation. The eggs are 
pelagic, and have usually one large oil globule, exceptionally more than one. 
(The buoyancy of the egg is in the paper attributed to the oil globule, an error 
which has been repeatedly made ; there are many pelagic ova which have no oil 
globule.) The eggs are somewhat oval in shape and slightly variable in size. 
Length of longer axis, -655 to 731 mm.; of shorter, -040 to 716 mm. Hatching 
took place in 5^ to days, at a temperature of 51° to 62° F. In the newly 
hatched larva the rectum is immediately behind yolk, but not open, and not 
extending to the edge of the fin-fold. The eyes are slightly pigmented, and 
there are two small patches of pigment on the tail. The anus was not open 
seven days after hatching ; the mouth not open at hatching. Spawning took 
place in May and June. 

Motella argentea, Rhein. — The young in various stages were identified and 
described by A. Agassiz, July 1882, in Young Stages, pt. iii. (Proc. Amer. 
Acad. Arts and Sci., vol. xvii.). In the youngest stage, 4 mm. in length, the 
embryonic fin-fold is continuous, notochord multicolumnar (a point not ascer- 
tainable from Brook's figures), pelvic fins palmate and large. In oldest stage, 
3*4 cm. in length, two dorsal and one anal fin all distinct; pelvic fins very long 
and narrow. There is some uncertainty about the identity of the specimens; 
they may belong not to Motella argentea, but to some species of Onus. 



EGGS AND LARVAE OF TELEOSTEANS. 115 

Eggs taken by the tow-net at Newport, identified as belonging to Motella 
argentea, are described by Agassiz and Whitman in Pelagic Stages of Young 
Fishes. The identification is based on the character and distribution of the 
pigment in the larva hatched from the eggs, and is to some extent doubtful. 
The average size of the eggs is *78 mm. There is a single oil globule (in one 
case two, which coalesced) which is large and colourless, and measures '15 to 
•16 mm. in diameter. The figure given of the newly-hatched larva agrees 
closely with Brook's figure of Motella mustela. The embryonic period varied 
with the temperature from three to six days. The eggs were taken from May 
to July. 

Motella cirnbria, Nilsson (Linn.). — The four-bearded rockling. Parnell's 
example, captured in June, had the ova almost mature. Three specimens 
were taken by me, in the trawl, off Fast Castle Point, Haddingtonshire, March 
12, 1886. In these the reproductive organs were very small. The largest 
specimen was '26 m. long. 

A species allied to Motella, probably actually a species of that genus, is 
figured in Pelagic Stages, pi. xii. The ovum is "70 mm. in diameter, and has 
a single oil-globule. The newly hatched larva agrees with that of Motella 
mustela, in that the rectum terminates, apparently blindly, immediately behind 
the yolk, and does not extend to the edge of the ventral fin-fold. The eggs 
were obtained in March and April. Another species allied to Motella is 
figured in Pelagic Stages, plate ii. figs. 1 to 3. 

The ovum of Merlucius is mentioned and figured by Kingsley and Conn,* 
but the size is not stated. Like that of Motella, it has a single large oil 
globule at the vitelline pole. 

The eggs and larvae of Lota vulgaris, the burbot, have been described by 
Carl J. Sundevall in Svenska Vetensk. Akad. Hand., 1855. The species is 
entirely confined to fresh water, and is thus unique among the Gadidse, all the 
rest of which are marine and produce pelagic ova. The ova of Lota are shed 
separate and loose at the bottom of the water ; some ova are opaque, some 
transparent. According to Sundevall, they are small, but measurements are 
not given. Figures of the newly hatched larva and somewhat later stages are 
given ; the drawings are not quite adequate, but show some essential points. 
In the newly hatched larva there is a single oil globule in the yolk, and there- 
fore probably in the ovum ; the anus is close behind the yolk, but not in contact 
with it ; the larva is 3 mm. in length. This larva bears a close resemblance to 
that of Motella, as figured by Brook. There are two differences in Lota ; the 
oil globule is not so far back, and the two transverse stripes of pigment in the 
tail of Motella are wanting. The pigment in an eight days old larva of Lota 

* Memoirs of Boston Society of Natural History, vol. iii. No. 6, 1883. 



110 MR J. T. CUNNINGHAM ON THE 

formed a series of spots along the dorsal edge of the side of the body and tail. 
This case is interesting, as showing how little modification is necessary to adapt 
the ova of two allied fishes to such apparently different environments as the 
surface of the sea and the bottom of a river or stream. The ova of the cod 
sink in fresh water, but they probably would not develop in that condition. 
The ova of Trigla gumardus sank in the water of the Scottish Marine Station, 
but they invariably died in that condition after some days. The conditions in 
which the ova undergo development are not constant in a given family, but the 
structure of the ovum is more so, and the structure of the larva is alwavs 
characteristic of families, and even, to some extent of whole orders. 

Fam. 3. Ophidiid.®. 

The eggs of Fierasfer {mm and dentatus) have been described by Emery in 
his Naples Station monograph on the genus. The ovum has a single large oil 
globule ; it is small. - 8 mm. in diameter. The ova when deposited are united 
together in masses, each mass containing many thousand eggs in a thick gela- 
tinous envelope. The masses are pelagic, floating at the surface of the sea. 
In the newly hatched larva the anus is in immediate proximity to the yolk, 
which still contains its oil globule situated at the anterior end. A great deal 
of pigment along the sides of the trunk, and a single row of chromatophores 
on each side at the ventral edge of the tail. A little in front of the level of the 
anus a median dorsal papilla interrupts the continuity of the fin-fold. This 
papilla grows rapidly, and ultimately forms a long filament supported on a 
short upright stalk. The filament bears a number of leaf-like appendages, and 
is called the vexillum. No stages of embryonic development are figured, and 
in the figures of the larva the internal structure is not shown. The structure 
of the notochord cannot be seen. A very lucid and complete account is given 
of the ovarian development of the ovum. The vitelline nucleus is described, 
and shown to be merely the starting point of the development of the vitelline 
spheres, which by their coalescence form the yolk in the mature ovum. The 
oil globule similarly arises from the coalescence of a number of small ones. 
The differences in the structure of mature ova are thus explained, and no 
support is given to the ideas recently advanced concerning the origin of the 
yolk from follicular cells, or of the latter from the germinal vesicle. 

Fam. 4. Macrurid^e. 
Development not yet studied. 



EGGS AND LARVAE OF TELEOSTEANS. 117 

Anacanthini Pleuronectoidei. 

Fam. PLEURONECTIDiE. 

The development of a great number of species belonging to this family 
has been studied. In the preceding section of this memoir, ova of four 
species of Pleuronectes are described. Mention of the study of several 
species has been made by M'Intosh. In Appendix F. of the Third Annual 
Report of the Scottish Fishery Board, he states that the ova of the cod, 
haddock, whiting, grey gurnard, common flounder, turbot, sole, lemon dab, 
common dab, and long rough dab had been examined in the Marine Labo- 
ratory at St Andrews. E. E. Prince describes the ova of Pleuronectes platessa, 
P. Jlesus, P. limanda, as well as those of Gadus ceglejinus, G. morrhua, G. 
merlangus, and Trigla gurnardus, in Ann. and Mag. Nat. Hist., May 1886, but 
gives no figures. The young of. Pleuronectes Aniericanus, Walb., are described 
and figured by Agassiz in Young Stages, plate ii„, from a stage at which the 
larva is 4 mm. in length. The eggs and newly hatched larva of this species 
are figured in Pelagic Stages, plate xvi. In the larva the rectum is, as far as 
can be judged from Agassiz's figure, a little distance behind the yolk, and 
the notochord seems to be unicolumnar ; but on neither of these points is the 
figure very distinct. In all the species of Pleuronectes which I have figured 
the rectum is in contact with the yolk, and the notochord multicolumnar. 

Pseudorhombus. — The eggs and larvae of Pseudorhombus oblongus, Storer, 
the Sienna flounder, are figured by Agassiz in Young Stages, ii. plate ix. 
figs. 1-3, and in Pelagic Stages, plates xiv., xv., figs. 1-14. There is one oil 
globule, which in the newly hatched larva is at the posterior end of the yolk ; 
at the same stage the rectum is in contact with the yolk. The character of 
the notochord is not shown in the figures. The egg of the transparent 
flounder, Pseudorhombus oblongus, Stein, has no oil globule, and no pigment 
on the yolk. The figures 1-4 on plate vi. of Young Stages, ii., given under 
the name of P. melanog aster, Stein, really belong to Tautoga onitis. 

Rhombus maculatus, Mitch. — Some advanced larvse of this species are 
figured in Young Stages, ii., but the eggs and newly hatched larva are not 
given. 

Hippoglossoides limandoides. — I have been unable to obtain eggs of this 
species. Many specimens were obtained in the months of May and June, 
which were spent ; occasionally a ripe male was obtained, but never a ripe 
female. It probably spawns in the neighbourhood of the Firth of Forth 
in April. M'Intosh states that he obtained the ova of this species before 
1st June 1884, but he does not describe them. (Second Annual Report, 
S. F. B.) 



118 MR J. T. CUNNINGHAM ON THE 

Arnoghssus megastoma, Donovan. — A specimen of this species, taken 16 
miles E. by N. of May Island, April 30, 1886, in the trawl, was brought to the 
station. The ova Avere quite immature. Thompson at Belfast, according to 
Day, ascertained that it spawned in October. 

Plagusia. — The young, about 1 inch long, is figured by Agassiz in Young 
Stages, ii., but not the eggs or larvae. 

Thus all the Anacanthini, as far as at present known, except Lota, have 
pelagic ova, and in all the rectum at the time of hatching is in contact with 
the yolk. In Gadus and Motella the anus is not open, and does not extend to 
the margin of the ventral fin-fold. 



Order III. ACANTHOPTERYGII. 

Div. I. Perciformes. 

Fam. 1. PercidtE. 

The young of Lahrax lineatus, Bl. and Schn., are figured by A. Agassiz in 
Young Stages, iii. In the youngest stage figured, 3 5 mm. in length, the yolk 
sac is already absorbed. The larvae were taken at the surface of the sea with 
the tow-net, but the eggs were not found. The ova of Perca fluviatilis are 
adhesive, and attached to fresh-water plants. An account of them is given by 
Sundevall. Hatching occurred fourteen clays after fertilisation. The newly 
hatched larva was 5 mm. long ; there was a single oil globule in the yolk sac, 
and the anus was slightly separated from the latter. Spawning took place in 
May. 

The ova of Serranus cabrilla are stated by Hoffmann to be pelagic. 



Fam. 2. Squamipennes. 
„ 3. Mullid/e. 
,, 4. Sparid^e. 



Fam. 5. Cirrhitid^;. 

6. SC0RPiENID/E. 



This family consists exclusively of marine fishes, and all the species that 
have hitherto been studied from the embryological point of view have 
pelagic ova. 

An account of the ovum of Scorpama is given in Hoffmann's memoir, 
published in the Transactions of the Amsterdam Academy, 1881. The species 
observed were S. porcus and >S'. scrofa. The ripe ovum before fertilisation 
consists of a perfectly homogeneous glassy yolk surrounded by a thin envelope 



EGGS AND LARVAE OF TELEOSTEANS. 119 

of protoplasm, which has a faint reddish tinge, and is as usual principally 
accumulated at the micropylar pole. The ovum before fertilisation has a 
slightly oval form, "95 mm. by *84 mm. in diameter. After fertilisation the 
perivitelline space is very small. Hoffmann deals only with fertilisation and 
segmentation, and gives no figures or descriptions of embryos or larvse. His 
examination of the ova of Scorpoena was made at Naples. The ova of 
Scorpsena are deposited in masses, each mass consisting of a large number of 
ova enveloped by a slimy substance. Hoffmann believes that the slimy sub- 
stance is not a product of the egg-membrane, but probably the peculiarly 
modified connective tissue of the them folliculi. This conclusion seems 
extremely unlikely, but no investigator has yet inquired into the origin of the 
gelatinous envelopes which contain the ova of Scorpcena or of Fierasfer. The 
newly hatched larva of Scorpcena is 2-07 mm. in total length, and the anus is 
almost in contact with the yolk sac, -07 mm., according to Hoffmann,, being 
the distance between the two. 

Hemitripterus americanus, C. and V. (H. acadianus, Storer.) — The ova 
and larvse of this species are described by A. Agassiz in Pelagic Stages. 
The ovum is pelagic, and possesses a single oil globule, which in the early stages 
of development is at the pole of the yolk opposite the centre of the blastoderm. 
Diameter of ovum, 1*02 to 1*10 mm. The developing embryo is distinguished 
by the large number of brownish-yellow chromatophores which, interspersed 
with a few black ones, are present on the sides of the body of the embryo, 
and over the whole surface of the yolk. In the newly hatched larva the 
rectum is separated by a very slight interval from the yolk. The fin-fold is 
very wide, and in it are three pigment patches — two dorsal and one ventral. 
The anus is apparently not perforated. The structure of the notochord is not 
shown. The identification of these ova and embryos seems to be based on the 
characters of the older stages of the larvae 



Fam. 7. Nandhle. 
„ 8. Polycentrid^e, 
„ 9. Teuthidid^ 

Div. II. Acanth. Beryciformes. 
Fam. 1. Berycid^e. 

Div. III. Acanth. Kurtiformes. 
Fam. 1. Kurtid^e. 



120 MR J. T. CUNNINGHAM ON THE 

Div. IV. ACANTH. POLYNEMIFORMES. 

Fain. Polynemid^e. 

Div. V. ACANTH. SdiENIFORMES. 

Fam. 1. Sclenid^e. 

Div. VI. ACANTH. XlPHIIFORMES. 

Fam. 1. XiPHiiD^E. 

Div. VII. Acanth. Trichiuriformes. 
Fam. 1. Trichiurid^e. 

Div. VIII. Acanth. Cotto-scombriformes. 

Fam. 1. Acronurid^e. 
„ 2. Carangid^e. 

Capros, according to Day, was observed to shed pelagic ova by Mr Dunn 
at Megavissey, July 20, 1882. 

Temnodon saltator, Linn. (Pomatomus saltatrix, Gill), is called the Blue- 
fish on the Atlantic coast of the United States. Pelagic ova, believed 
to belong to this species, are described by Agassiz in Pelagic Stages, 
and a long larva, 9 mm. in length, identified as Temnodon, is figured in Young 
Stages, pt. iii. pi. ii. The ova to which I have referred are, in one respect, 
unique among all the kinds of pelagic ova hitherto described. In Agassiz's 
own words, the egg exhibits a partial segmentation of the yolk — that is to say, 
at the stage when the embryonic ring has just been formed, there is a ring of 
definitely limited large cells round the edge of the blastoderm. After the 
blastoderm has enclosed the yolk, the large cells seem to form a complete 
envelope round the yolk beneath the blastoderm. To judge from the figures 
given by Agassiz and Whitman, I should have concluded that in this species of 
ovum the periblast, instead of being a syncytium, was divided into cells, and 
should have been ready to agree with the view expressed by those authors in 
their " Preliminary Notice" (Proc. Amer. Acad. Arts mid Sci., vol. xx.), namely, 
that the actual cleavage of the yolk in this instance was positive proof that the 
nucleated periblast in all cases, and the yolk, are " integrant portions of the 
ovum." But in Pelagic Stages it is stated that closer examination has shown 



EGGS AND LARVAE OF TELEOSTEANS. 121 

that the large cells are situated beneath the periblast, and belong to the yolk ; 
that they are not protoplasmic elements, but vitelline, although they have an 
epibolic growth, and extend round the unsegmented yolk as this becomes 
enclosed by the blastoderm and periblast. It is pointed out that the change in 
relations of these superficial yolk segments shows that a transposition occurs in 
the Teleostean ovum among the yolk elements closely analogous to the in- 
vaginatory movement of the yolk in holoblastic ova. The diameter of the 
ovum is "70 to 75 mm. The ova occur at Newport from the middle of June to 
middle of August. At the yolk pole there is a single large oil globule. The 
newly hatched larva is 2*15 mm. in diameter; the rectum is separated by a 
distance of *275 mm. from the yolk sac; pigment is scanty; a series of black 
chromatophores along the dorsal edge of the tail, and a few brownish-yellow 
ones along the body and rectum. The structure of the notochord is not shown. 
The development of the young fish was traced till a stage at which it measured 
9 mm. in length. 

The presence of an oil globule, the externally segmented yolk, and the slight 
separation of the rectum from the yolk sac, are the diagnostic features in 
Temnodon, but how far these are characteristic of the family is not known. 

Fam. 3. Cyttid.e. 
„ 4. Stromateid^e. 

This is a small family of marine fishes, containing only two genera. 
Figures of Stromateus triacanthus, Peck, from a length of 7 mm. upwards, are 
given by Agassiz in Young Stages, pt. iii. The notochord is apparently 
multicolumnar, but no other embryonic or larval characters are to be discovered 
from the figures. The species is called Butter-fish in America, and the young 
at the length of 10-20 mm. are in the habit of sheltering themselves beneath 
the umbrella of Dactylometra, one of the Scyphomedusae. 

Fam. 5. Corypilenid^e. 
„ 6. Nomeid^e. 

,, 7. scombrid.e. 

According to Day, the eggs of Scomber scomber, the common mackerel, are 
shed in May and June, and in the Brighton Aquarium have been observed to 
be of the pelagic kind. The development of Cybium maculatum, the Spanish 
mackerel, has been described by John A. Eyder (Bull. U.S. Fish Commission, 
vol. i., 1881). The investigation was carried out in July 1880 at Mobjack Bay, 
Virginia, and in 1881 at Cherrystone Harbour, Va. The eggs hatched twenty- 
four hours after fertilisation, but the temperature to which they were exposed 
is not stated. Evidence was obtained that spawning naturally takes place at 

VOL. XXXIII. PART I. Q 



122 MR J. T. CUNNINGHAM ON THE 

night. The ovum measures ^§ to £$ mcu m diameter, or, as measured from the 
figures given, '856 to 1*06 mm. It is pelagic; there is a single large oil 
globule, otherwise the yolk is homogeneous ; the perivitelline space is small. 
The newly hatched larva is 2-52 mm. long as measured from the figure ; the 
notochord is multicolumnar ; the anus immediately behind the yolk, and open ; 
pigments spots are present on the body and round the oil globule, and 
also form one conspicuous transverse stripe in the middle of the tail. The oil 
globule in the hatched larva is situated on the ventral side of the yolk, a little 
posteriorly. The mouth opens twenty-one hours after hatching. 

Fam. 8. Trachinid^;. 

The development of Tracliinus vipera has been described by Geo. Brook 
{Lin. Soc. Jour., vol. xviii., 1884). The eggs were shed in that author's 
aquarium. Spawning takes place at night, and is continued through the 
months of May, June, and July. The ovum is pelagic, 1 32 mm. in diameter, 
and contains from 20 to 30 small oil globules. The oil globules are external to 
the vitellus, and contained in depressions of its surface. It is probable that this 
is often the case ; it certainly is in Trigla gurnardus, but whether the oil 
globules are always external is doubtful. The perivitelline space is small. 
Hatching took place on ninth, tenth, and eleventh clays, at a temperature of 54° 
to 60° Fahr. In the newly hatched larva the rectum is immediately behind the 
yolk sac, the notochord multicolumnar. The eyes are pigmented; black pig- 
ment cells are scattered over the body and the surface of the yolk sac, and 
aggregated in a transverse stripe at the middle of the tail. The ventral fins are 
well developed at the time of hatching. The length of the newly hatched larva 
is 3 5 mm. The yolk sac is absorbed, and the mouth well developed twenty- 
four hours after hatching. 

Fam. 9. Batrachid^:. 

The young Batrachus tau, Lin., 2 mm. in length, has been figured by 
Storer (Mem. Amer. Acad., v. pi. xix.). Agassiz figures a specimen 6 mm. 
in length in Young Stages, pt. iii., but this shows only traces of the larval 
characters. The anal is still continuous with the caudal fin, and the " ganoid " 
lobe of the tail is well marked. 

Fam. 10. Pediculati. 

The eggs of Lophius piscatorius, Lin., are described in Young Stages, pi. 
iii. The eggs are held together by gelatinous mucus in a single flat layer 
which floats horizontally in the sea, forming a large sheet 3 feet broad and 
'I") to 30 feet long. The spawn is shed on the American coast from June to 



EGGS AND LARVAE OF TELEOSTEANS. 123 

August. It has also been observed on the British coast, but I have not myself 
met with it. A more complete description, with better figures, is given 
by Agassiz and Whitman in Pelagic Stages. The egg is large, 175 mm. 
in diameter, and has a single immense oil globule "4 mm. in diameter, of a 
transparent copper colour. Black chromatophores are developed very early, 
and are aggregated chiefly about the ventral side of the embryo, present in less 
abundance on the surface of the yolk sac, round the oil globule, and on the tail. 
In the newly hatched larva the yolk sac is globular, and very large in compari- 
son with the body ; the oil globule is ventral and posterior ; the rectum 
is immediately behind the yolk ; the eyes are deeply pigmented ; the notochord 
multicolumnar ; the pelvic fins not developed. The successive forms of the 
larva, which is up to a late stage pelagic, are described and figured in Young 
Stages, iii. Agassiz points out the resemblance, both in the character of the 
spawn and the structure and development of the larva, between Lophius and 
Fierasfer, comparing the long anterior dorsal spine in the former, which is 
a permanent organ, but develops at a very early stage, to the vexillum 
of Fierasfer, which is a temporary appendage disappearing completely in the 
adult. It seems probable that in the Fierasfer larva the vexillum is morpho- 
logically derived from a fin ray, as are the appendages in Lophius. 

The male of Antennarius, another species of this family, a pelagic fish, 
makes, according to Gunther, a nest, and guards the eggs deposited in it. We 
have thus in this family a series of steps in the transition from ordinary littoral 
adhesive ova to typical pelagic ova. The ova of Antennarius are probably 
adhesive, and are deposited in a pelagic nest. The ova of Lophius are also 
adhesive, but float as a detached mass unprotected by an apparatus formed 
from pelagic algae. If the ova of Lophius were separate, instead of adhering 
together in a mass, they would be typical pelagic ova. 

Fam. 11. Cottid^e. 

The question of the ova of Cottus has been discussed in a previous section. 
The pelagic ova of Trigla gurnardus have been described.* 1 In this family we 
have a greater difference between the ova of closely allied genera than in the 
preceding, for the eggs of Cottus are typical examples of littoral adhesive ova, 
while those of Trigla are typically pelagic. Sundevall (Joe. cit.) gives an 
account of the development of Cottus gobio and Cottus quadricornis. The eggs 
of the former species are deposited in May. The larva twenty-four hours after 
hatching was 8 mm. long; there was a single oil globule in the yolk, and the 
rectum was in contact with the yolk sac. The larva of Cottus quadricornis is 



* u 



Yolk and Gastrula," J. T. Cunningham, Quart. Jour. Micr. Sci., 1885. 



124 MR J. T. CUNNINGHAM ON THE 

very similar; its length three days after hatching was 11 "5 mm. The eggs of 
both species are adhesive, and form masses sticking to objects on the shore. 

Fam. 12. Cataphracti. 

The fertilised ova of Agonus cataphractus have never been described; 
but Prof. M'Intosh, in 3rd Ann. Rep. S. F. B., says he found nearly mature ova 
in a specimen trawled near St Andrews on March 12. The ova had a pale 
salmon colour, were 1*3 mm. in diameter, and probably adhesive. 

Fam. 13. Pegasid^e. 



Div. IX. ACANTH. GOBIIFORMES. 

Fam. 1. Discolali. 

The ova of Cyclopterus lumpus have been mentioned in the previous section. 
Liparis is the only other genus, and what is known of the spawn of Liparis 
Montagui has also been stated. 

Fam. 2. Gobiid^e. 

Gobins Ruthensparri is stated by Day to have been bred in confinement by 
Mr Roberts of the Scarborough Museum. The ova were adhesive, and were 
deposited within the shell of a barnacle. The male watched over the mass of 
eggs, and fanned them with his fins. 

Hoffmann (loc. cit., p. 19) gives a description and figure of the ovum 
of Gohius minutus. The ovum has a peculiar elongated pyriform shape, with a 
very large perivitelline space, and at the narrow end are a number of filaments, 
in the centre of which is the micropyle. The eggs are attached by the 
filaments. 

The ova of Callionymus lyra are pelagic, and have been described by 
M'Intosh, in Ann. and Mag. Nat. Hist., Dec. 1885. On the 8th August a 
female specimen was obtained at St Andrews, from which ripe ova could be 
pressed out. The ova are pelagic, transparent and buoyant, small in size, being 
of about the same diameter as the ova of Pleuronectes flesus. The exterior 
surface of the vitelline membrane or zona racliata exhibits a reticulum of 
slightly elevated ridges, the meshes of the reticulum being hexagonal; from 
this characteristic the ova can be easily identified. At Millport, in June of the 
present year, I obtained a pelagic ovum from the tow-net which agreed exactly 
with Prof. M'Intosh's description. M'Intosh adds, that Trophon, hermit 
crabs, and bivalve mollusca were found in the stomach of Callionymus. He 
gives no figures or description of any embryonic or larval stages of the species. 



EGGS AND LARV^3 OF TELEOSTEANS. 125 

There is here another example of a family in which some genera produce 
adhesive, others pelagic, ova. 

Div. X. Acanth. Blenniiformes. 

Fam. 1. Cepolid^e. 

„ 2. Heterolepidotid^e. 
„ 3. Blenniidje. 

The ova of Anarrhichas lupus have been discovered by Prof. M'Intosh to be 
deposited in February ; they are large, heavy, and non-adhesive, and the larvae, 
when hatched, are well advanced in development (see Nature, June 17, 1886). 

The ova of Blennius galerita, according to Day, are adhesive, and attached 
to the under surface of stones. 

Blennius pholis also deposits adhesive ova, which are attached to small 
caverns in the rocks of the sea-shore. 

The ova of Blennius are stated by Hoffmann to possess processes extend- 
ing from the zona radiata. 

The ova of Centronotus gunnellus, according to W. Anderson Smith, are 
deposited from February to April. The ova are adhesive, and form a spherical 
mass about the size of a walnut ; this ball is quite free, and both parents lie 
coiled round it. 

In Zoarces viviparus the ova are retained during development within the 
cavity formed by the coalesced ovaries. Breeding takes place in the winter 
months, chiefly in December, January, and February. Specimens in which the 
young were ready to be born were obtained on the shore at Granton in 
February and March. The young at parturition are about 1^ inches long, and 
in all respects, except size, similar to the parents. I met with several 
specimens in which the young in the ovary had been killed by some cause or 
another, and when the cavity was cut into, their bodies were discovered in a 
shrunken state, but not decomposed. 

Fam. 4. MastacembelidjE. 

Div. XL ACANTHOPTERYGII MuGILIFORMES. 

Fam. 1. Sphyr.enid,e. 
„ 2. Atherinid^e. 

Several stages of Atherinichthys notata, Gunther (Chirostoma notata, Gill), 
are figured by Agassiz in Young Stages, pt. iii. In the youngest the embryonic 
fin-fold is still unaltered, but the yolk sac is absorbed, and the mouth open. 



126 MR J. T. CUNNINGHAM ON THE 

The ovum of this species is stated by Ryder to possess four filamentous 
processes connected with the vitelline membrane ("Development of Belone 
longirostris" Bull. U.S. Fish Commission, vol. i.). The threads or filaments are 
more completely described by Ryder in vol. ii. of the same bulletin, the 
fish being there called Menidia, which is a synonym. The threads are in length 
about eight times the diameter of the ovum, and when the latter is first 
emitted the threads lie coiled spirally round it. There can be little doubt that 
the four threads are merely the outer layer of the zona radiata in a specialised 
form, and are homologous with the suspensory membrane in Osmerus. 

Fam. 3. Mugilhle. 

Div. XII. Acanth. Gastrosteiformes. 

Fam. 1. Gastrosteid^e. 

The ova of Gastrosteus are adhesive, and deposited in nests made with water 
plants, and guarded by the male. Spinachia vulgaris makes nests of seaweeds, 
Fucus, &c, on the sea-shore ; its ova are similar to those of Gastrosteus, but 
larger. It has been shown by Prof. Karl Mobtus of Kiel, that the white fila- 
ments, by which the nest of Spinachia is held together, are spun by the male 
fish, and that they are formed from a substance resembling mucin which is pro- 
duced in the kidneys (see Schr. Naturwiss. Vereins fur Schleswig Holstein, Bd. 
vi., 1885; translated in Ann. and Mag. Nat. Hist., Aug. 1885: also E. E. 
Prince, Ann. and Mag., Dec. 1885). The ova of Spinachia, according to 
Prince, are "085 inch in diameter. A large mass of pale yellow oil globules 
are aggregated at the yolk pole. At temperature 41° to 51° Fahr., in June the 
ova hatched in twenty-five to forty days. No figures of the development are 
given by Prince. 

Fam. 2. FiSTULARiiDiE. 

Div. XIII. Acanth. Centrisciformes. 
Fam. 1. Centriscid^e. 

Div. XIV. ACA.NTH. GOBIESOCIFORMES. 

Fam. 1. Gobiesocid^e. 

Lepadogaster Decandolii. — Some observations on the development of this 
species are described by W. Anderson Smith in Proc. Roy. Phy. Soc. Edin., 
1886. The ova are adhesive, attached to stones or shells, and watched over 



EGGS AND LAKV^ OF TELEOSTEANS. 127 

by both parents. Spawning takes place in June and July on the west coast of 
Scotland. The ovum has a single oil globule, and is hatched twenty-eight days 
after fertilisation. The ovum of L. bimaculatus are always found adhering to 
the inner surface of shells of Pecten operculatus; they are deposited likewise in 
June and July, and are guarded by at least one of the parents. 

Div. XV. Acanth. Channiformes. 
Fam. 1. Ophiocephalim:. 

These are fresh-water fishes of the Indian region. The male Ophiocephalus 
is stated by Gunther to make a nest and guard the presumably adhesive ova. 

Div. XVI. Acanth. Labyrinthibranchii. 

Poly acanthus mridiauratus, Gunther, the Macropus viridi-auratus of 
Lac^pede, commonly called the Paradise-fish, is a native of the East Indian 
Archipelago, but is commonly kept in aquaria in Europe, and breeds freely in 
confinement. Some account of the ova is given by Dr Miecz. von Kowalewski 
in Zeit. f. wiss. Zool., Bd. xliii. The perivitelline space is small ; the yolk 
apparently broken up into small masses, and large oil globules are present; but 
the appearance of the living ovum is not described. 

Order II. ACANTH. PHARYNGOGNATHI. 

Fam. 1. POMACENTRIDiE. 

The ovum of Heliasis chromis is described by Hoffmann (loc. cit., p. 19). 
The name he uses seems to be slightly erroneous. It is the Heliastes 
chromis of Giinther's British Museum catalogue. The ovum forms a some- 
what long ellipsoid with blunt ends, and at one of the poles is a group of 
eight or nine long straight filaments attached at their basis to the vitelline 
membrane. The micropyle is situated in the centre of the group of filaments. 
Hoffmann remarks that the filaments in this ovum, and in Belone, Blennius, 
Gobius, represent the external zona in adhesive ova such as Leuciscus and 
Perca, in which the zona radiata is differentiated into two layers. On the other 
hand, in pelagic ova, such as those of Scorpama, or in heavy non-adhesive ova, 
such as those of Salmo, no division into two layers can be discovered in the 
zona radiata. We may add to this comparison of Hoffmann's that it is pro- 
bable from what Ryder observes concerning the development of the filaments 
in Belone, that these processes are actually formed by a splitting up and 
unequal development of the external zona ; and thus there is no fundamental 
difference between the origin of the suspensory membrane in Osmerus eperlanus 
and the filamentous processes in Belone, Atheinnichthys, Heliastes, &c. The 



128 MR J. T. CUNNINGHAM ON THE 

yolk of Heliastes resembles in structure that of the herring, being composed of 
a number of ellipsoidal vitelline discs; but there is also present a large oil globule 
at the vitelline pole. The protoplasm in the mature unfertilised ovum forms as 
usual an envelope round the vitellus which is thickest beneath the micropyle, 
and thins away all round that point. The blastodisc and blastoderm during 
simple segmentation is large in proportion to the yolk. The perivitelline space 
is considerable. Hoffmann gives no figures of the embryonic or larval stages. 

Fam. 2. Labrid^e. 

The development of a large number of the wrasses has been studied. 

Tautoga onitis, Linn. — The pelagic ova of this species are described and 
figured in Pelagic Stages. The diameter of the ovum measures '90 to "95 mm. 
The yolk is homogeneous, and there is no oil globule ; the perivitelline space 
is of moderate dimensions. The newly hatched larva is 3 05 mm. in length; 
the rectum is not in contact with the yolk sac, but at a distance of *55 mm. 
from it (not nearly so far back as in Clupea). The anus is open, the notochord 
multicolumnar ; the eye is scarcely pigmented, but there are small compact 
pigment spots along the dorsal region of the sides of both body and tail ; the 
pectorals are scarcely developed, the ventrals not at all. The eggs of Tautoga 
were artificially fertilised, so that the identity of the ova and newly hatched 
larvie is certain. But the authors point out that the ova of Ctenolabrus, 
Ps. melanogaster, and Tautoga are so similar, both in structure and size, that it 
is scarcely possible to distinguish them with certainty in the produce of the 
tow-net. The authors state that figs. 1, 2, 3, and probably fig. 4 (in my 
opinion fig. 4 also, certainly) in plate vi. of Young Stages, part ii., belong to 
Tautoga, and not to Pseudorltombus melanogaster. Thus the position of the 
rectum with respect to the yolk sac in the newly hatched larvae is shown 
to be a constant family character ; and there is no exception to the statement 
that in Pleuronectidge the rectum at that stage is in contact with the yolk sac. 

Ctenolabrus adspersus, Walb. (C. coeruleus, Storer). — The ova of this 
species have been described by Agassiz and Whitman in Pelagic Stages, and 
by Kingsley and Conn. The ovum is "85 to "92 mm. in diameter. Before 
fertilisation the peripheral layer of protoplasm is densely filled with refractive 
granules, which render the ovum opaque; but after fertilisation the granules 
disappear, and the egg becomes perfectly transparent. In the newly-hatched 
larva the rectum is separated by *25 mm. from the yolk sac, the total length of 
the larva being 2*30 mm. There are black dendritic chromatophores along the 
sides of the body and tail. The time required for hatching varies from two to 
six days. The eggs are shed at Newport in the months of May and June. 

The ova of Julis vulgaris are described by Hoffmann (loc. cit., p. 43). The 
diameter of the ovum measures 75 mm. The yolk is homogeneous, but con- 



EGGS AND LARV^ OF TELEOSTEANS. 129 

tains an oil globule '15 mm. in diameter. The ova are suspended separately in 
the water not united in masses. The dimensions of the newly-hatched larva 
are 1*77 mm. in total length, 15 mm. from the yolk sac to the anus. 

The ova of Grenilabras, of which genus Hoffmann examined four species, 
are not pelagic, but adhesive. The zona radiata shows the division into two 
layers, which occurs in most adhesive ova. The diameter of the ovum is *7 to 
"75 mm. The yolk is not homogeneous, but contains a number of vitelline 
globules ; there seem to be no oil globules. The newly-hatched larva is 
3*6 mm. long, and the anus is "6 mm. from the yolk sac. 

Thus we see that considerable variations occur in the family of Labridse in 
the character of the ova. Most of the genera produce pelagic ova, but the ova 
of Crenilabrus are adhesive. As in the Gadidse, there is either a single oil 
globule in the yolk or none at all. Two characters seem constant throughout 
the family — (1) that the notochord is multicolumnar, (2) that the anus is at 
some little distance from the yolk sac, though not nearly so far back as on the 
Physostomi. The separation of rectum and yolk sac occurs also in the Carangidae 
(Te?nnodon),&nd among the Physoclisti seems to be confined to these two families. 

Fam. 3. Embiotocid^e. 

Fishes of the North Pacific, most abundant on the American coast. 
All viviparous. 

Fam. 4. Chromides. 

Order V. LOPHOBRANCHII. 

Fam. 1. Solenostomid^e. 

According to Gunther, the female bears the eggs attached to filaments 
developed on the ventral fins, the inner edges of which are united to the skin of 
the body. 

Fam. 2. Syngnathid^e. 

In Siphonostoma typhle, which is common on the British coasts, the ova are 
carried till the time of hatching by the male in a pouch formed by longitudinal 
folds of the skin behind the anus. 

In Syngnathus there is a similar pouch in the male. According to Ryder, 
yolk contains numerous oil globules. 

In Nerophis the ova are attached to the abdomen of the male by a viscid 
secretion in front of the anus. N. lumbricAformis and N. aquoreus are not un- 
common on the east coast of Scotland, but I have not had an opportunity of 
examining the ova of either. 

Some account of the development of Hippocampus is given by John 
A. Ryder in Bull. U.S. Fish. Commission, Bd. 1. In the embryonic Hippo- 
cumpus the fin-fold is wanting, in Syngnathus it is but slightly developed. 

VOL. XXXIII. PART I. R 



130 MR J. T. CUNNINGHAM ON THE 

Order VI. PLECTOGNATHI. 
Fam. 1. Sclerodermi. 
„ 2. Gymnodontes. 

The development of these has not been studied. 

The Maturation and Fertilisation of the Teleostean Ovum. 

In considering the subject of the phenomena which take place in the ripe 
Teleostean ovum immediately after its separation from the parent, two ques- 
tions chiefly excited my curiosity, neither of which have I yet solved to my 
complete satisfaction. These questions refer to the account of the phenomena 
which has been given by Professor C. K. Hoffmann." The first is, Is there 
any foundation for Hoffmann's statement that the first segmentation spindle is 
directed radially, and divides into a superficial nucleus which belongs to the 
archiblast, and a deeper one which belongs to the periblast % The second is, 
Can we trace in the fish ovum the transformations of the nucleus which 
accompany the expulsion of the polar bodies, and compare these transforma- 
tions with those which E. van Beneden t has described in Asearis megalocephala. 

The subject of the last question will be considered first. The investigation 
of the matter is one of considerable difficulty. It is necessary, in the first 
place, to have a plentiful supply of healthy living specimens of some species 
with pelagic ova ; and in the second place, to have at command the most 
approved appliances and reagents for their microscopic examination. The first 
opportunity I had of making the attempt was in May of the present year, when I 
had a number of ripe Pleuronectes limanda alive in the aquarium of the Station. 

In the ripe ovum of P. limanda, immediately on its escape from the ovary, 
the zona radiata is in immediate contact with the ovum. The condition of the 
ovum is shown in Plate III. fig. 1. There is no doubt that the eggs of all the 
species of Pleuronectes and Gadus are closely similar except in size, and Ryder 
is in error when he indicates a peri vitelline space in his figure of the ripe newly 
shed ovum of the cod. There is a layer of protoplasm round the ovum in the 
neighbourhood of the micropyle, which thins out at the pole opposite the 
micropyle. In the living egg, within half an hour after it is shed, whether 
milt be added to the water in which it is contained or not, the expulsion of a 
transparent spherical polar body through the micropyle can be readily observed. 
Its appearance is shown in Plate II. fig. 10, taken from an unfertilised ovum, 
and Plate III. fig. 4, three hours after fertilisation. At this latter stage the 
perivitelline space has begun to appear ; it develops first in a ring round the 
micropyle as a centre. The protoplasm, immediately after the ovum is shed, 
begins to collect at the micropylar pole of the ovum, and this process begins 

* See Vcrhandelingen der Tconink. Alcad. der Wetenschappen, Th. xxi., Amsterdam, 1881. 
t La Maturation, Fecondation, etc., et hi Division Celhdaire, Paris et Gaud, 1883. 



EGGS AND LARVAE OF TELEOSTEANS. 131 

the rhythm of segmentation. At the stage shown in Plate III. fig. 3, one and 
a half hours after fertilisation, the central part of the protaplasmic disc is much 
the thickest, forming a somewhat conical protuberance downwards into the 
yolk. The protuberance afterwards disappears, and at the end of three hours 
the blastodisc has the shape shown in Plate III. fig. 4, the lower surface being 
uniform. Then a second aggregation of the protoplasm begins, but this time 
towards two points, as shown in Plate III. fig. 5, producing the first division of 
the blastodisc. Thus the aggregation of the protoplasm towards the micro- 
pylar pole may be regarded as a contraction towards one central point, and 
the first division as due to a contraction towards each of two separate points. 

The expulsion of a polar body through the micropyle I observed repeatedly 
in the ova of Pleuronectes cynoglossus studied at Millport last June. It took 
place in both fertilised and unfertilised ova. But I was unable to discover 
either in the living eggs, or in the fresh eggs treated with reagents on the slide, 
any nuclear spindle either before or during the expulsion of the polar body. In 
one or two instances I noticed a minute pyriform projection of protoplasm on 
the surface of the blastodisc after the latter had withdrawn itself from the 
vitelline membrane (Plate III. fig. 7) This might be either a second polar body, 
or simply the proximal part of the first drawn away with the receding blastodisc, 
from the inner end of the micropyle. Agassiz and Whitman, in Pelagic Stages, 
p. 19, mention the formation of two polar bodies in Teleostean ova, and under- 
take to describe them in a subsequent memoir. 

My results, as far as they go, concerning the unfertilised ova, are in agreement 
with those of Hoffmann. In the unfertilised ovum, as a rule, the expulsion of 
the polar globule through the micropyle and the concentration of the protoplasm 
take place just as in the fertilised ovum, with the exception that the latter 
process goes on much more slowly in the unfertilised ovum. I have never seen 
any traces of segmentation in the unfertilised ovum. The small proto- 
plasmic body on the blastodisc seen two hours after fertilisation, and shown in 
PI. III. fig. 7, was seen also at the same stage in the unfertilised ovum. The 
aggregation of the protoplasm in the fertilised ovum is finished about three 
hours after fertilisation, and the stage shown in PI. III. fig. 4, is reached. At 
this stage the unfertilised ovum stops unchanged, being perfectly incapable of 
segmenting. PI. III. fig. 9 shows an unfertilised ovum of PI. cynoglossus six 
hours after shedding, at which time the fertilised ova were in the eight-cell 
stage, and the cells again dividing to form the sixteen-cell stage. The 
unfertilised ova were in the condition shown in PI. III. fig. 9, twenty- four hours 
after being shed, and remained unchanged till they died. I was not able to 
determine with absolute certainty at what stage the spermatozoon entered the 
fertilised ovum. This occurs, as is evident from PI. IV. fig. 2, during the first 
half hour, and I am inclined to believe that it takes place immediately the ripe 



132 MR J. T. CUNNINGHAM ON THE 

ovum is exposed to the milt, so that the spermatozoon remains within the 
protoplasm while the polar globule or globules are being expelled. 

To take up now the first of my two questions. The changes which occur in 
the blastodisc after the ovum has been exposed to the influence of milt are 
shown in the figures of the ova of PI. limanda and PL cynoglossus. The separa- 
tion of the vitelline membrane from the blastodisc occurs almost immediately 
after the ovum has been placed in sea water containing milt. The protoplasm 
aggregates at the micropylar pole, and half an hour after fertilisation it projects at 
the pole considerably into the yolk (PI. III. figs. 3 and 8). At this stage, in ova 
treated with acetic acid and methyl green, I was able with a high power to see 
distinctly the male and female pronuclei in close proximity to one another (PI. 
IV. fig. 2). I was not able to discover the spindle produced from the union of 
these two bodies. The first segmentation of the blastodisc takes place gradually 
by the aggregation of the protoplasm round two centres, as in PI. III. fig. 5, and 
PI. IV. fig. 1. The protoplasm towards each side of the blastodisc projects 
downwards into the yolk, so that there are now two of these projections 
instead of one, with a deep broad furrow in the under surface of the blastodisc 
between them. No furrow on the upper surface of the blastodisc is at first 
visible. After treatment of the ovum with acetic acid and methyl green at this 
stage, a nucleus can be made out very distinctly in the two halves of the 
blastodisc, and these are the only two nuclei in the ovum. The line joining the 
nuclei is a chord of the sphere of the ovum, and not a radius, as stated by Hoff- 
mann. The nuclei are best seen when the ovum is placed on the slide with the 
blastodisc downwards, so that the blastoderm is seen through the transparent 
yolk, the stained ova being mounted in glycerine. It was from an ovum in these 
conditions that PI. IV. fig. 3, was taken, the ovum having been killed with 
acetic acid half an hour after fertilisation. The outline of the blastodisc on the 
surface of the ovum is not circular, but elliptical, and the plane of division 
passes through the short axis of the ellipse. This plane of division contains 
the principal axis of the ovum, by which I mean the axis passing through the 
centre of the blastodisc and the centre of the ovum. Hoffmann states that the 
plane of the first division is perpendicular to the principal axis of the ovum 
(he. cit., p. 105). It seems to me possible that Hoffmann may have been led 
into this error by the relative positions in which the two nuclei are seen when 
the ovum is in a certain position with respect to the axis of the microscope. To 
explain this I must refer to the diagrams shown in figs. 1 and 2. Fig. 1 
represents a section of the ovum passing through the principal axis and per- 
pendicular to the plane of the first division of the blastodisc. Now, if the axis 
of the microscope occupies, with respect to the ovum, the position x y, and the 
plane which is in focus, perpendicular of course to that axis, occupies the posi- 
tion shown by the line a b, then the appearance of the section of the ovum seen 



EGGS AND LARVAE OF TELEOSTEANS. 



133 



in this plane will be that represented in fig. 2. The two nuclei will be seen 
projected on to the focus-plane as at n l n 2 , fig. 2 ; while the under surface of that 
part of the blastodisc, which is nearer to the observer, will be projected on to 
the focus-plane as a curved line, apparently dividing the blastodisc into 
two portions, one internal and one external, each containing one of the nuclei. 
In PI. III. fig. 8, the blastodisc is seen thus apparently divided before the first 
division has taken place, but the dividing line is nothing but the under surface 
of the near part of the blastoderm projected on to the focus-plane. A com- 
parison between the diagram in fig. 2 and figs. 4 and 12, pi. iii. of Hoffmann's 

a 

y 




i 

Fig. 1. Fig. 2. 

memoir, will show how completely his views are explained by my supposition. 
At the same time all his figures cannot be so explained. Figs. 2 and 4 of his 
pi. v. are in direct opposition to my results. 

It is a remarkable fact that, as will be evident from a reference to PI. IV. 
fig. 3, the nuclei of the two-cell stage are not at first in the thickest part of their 
respective cells. The centre of aggregation of the protoplasm lies nearer the 
edge of the blastoderm than the nucleus, and it would seem as if the protoplasm 
were active in the division and the nucleus passive, a hypothesis quite contrary 
to current conceptions. I have been unable to find any evidence of the exist- 
ence of periblast up to the eight-cell stage. PI. IV. fig. 5, shows an optical 
section of the four-cell stage, in which it is evident there is no separate sub- 
blastodermic layer. 



134 



MR J. T. CUNNINGHAM ON THE 



Spawning Periods of 


SOWtf 


0/ the Fishes of the Firth of Forth 








1-3 




C3 




I— 1 


a5 




bb 


P-, 







> 



d 

CD 


Clupea harengus, L., 


J 


X X 


X X 










X X 


X X 


? 


? 


? 


Osmerus eperlanus, Lac., 
Gadus morrhua, L., 






X X 


X X 
X X 


















G. seglefinus, L., . 






X X 


X X 


















G. merlangus, L., . 






X X 


X X 


















Pleuronectes platessa, L., 

PI. flesus, L., ... 




X X 


X X 




















PL limanda, L., 










X X 
















PI. cynoglossus, L., 

PI. mici'ocephalus, L., . 










X X 


X X 














Trigla gurnardus, L., 








X X 


X X 


X X 


X X 












Zoarces viviparus, L., 
Spinachia vulgaris, 
Callionymus lyra, . 


X X 


X X 








X X 




X X 











Bibliography. 
The following list contains the titles of the memoirs and books used in the 
preparation of the preceding paper. It comprises all the works I have been 
able to discover which give speciegraphical details concerning ova or larvae : — 

1855. Carl Sundevall. Om Fisk Utveck, Svensk. Vetensh. Altad. Hand., vol. i., New Series. 
1867. A. W. Malm. Pleuronektidermas Utveck, Ibid., vol. vii. 

1877. A. Agassiz. Young Stages of Osseous Pishes — I. Devel. of Tail, Proc. Amer. Acad., vol. xiii. 

1878. A. Agassiz. Young Stages, &c. — II. Devel. of Flounders, Ibid., vol. xiv. 

1882. A Agassiz. Young Stages, &c. — III, Ibid., vol. xvii. 

1884. A. Agassiz and C. 0. Whitman. DeveL of some Pelagic Fish Eggs, Prelim. Notice, Ibid., 

vol. XX. 

1885. A. Agassiz and C. 0. Whitman. Devel. of Osseous Fishes — I. Pelagic Stages of Young Fishes, 

Mem. Mus. Comp. Zool. Kara., vol. xiv., No. 1, pt. i. 
1881. John A. Ryder. Devel. of Silver Gar (Belone longirostris), Bull. U. S. Fish. Com., vol. i. 
Dev. of Spanish Mackerel (Cybium maculatum), Ibid., vol. i. 
Devel. of Lophobranchiates (Hijypocampus antiquarum), Ibid., vol. i. 
Obs. on Embryo Fishes (Alosa sapidissima, tyc), Ibid., vol. ii. 
Devel. of Amiurus albidus, Ibid., vol. iii. 

Embryography of Osseous Fishes (Cod), Rep. U. 8. Fish. Com. for 1882. 
C. Kupffer. Entwickl. des Ostsee-herings, Aus. dem Jaresb. der Com. zur Tint, der Deutschen 

Meere, Berlin. 
C. Kupffer. Die Gastrulation au den meroblast. Eiern der Wirbelthiere, &c, Teleostei., Arch, 
f. Anat. und Phys., His and Du Eois Rcymond. 
1881. C. K. Hoffmann. Ontogenie der Knochenfische, Verh. Koninlt Alcad. van Wetens, Amsterdam, 
Deel xxi. 

1883. V. Hensen. Vorkommen und Menge der Eier einiger Ostseefische, i ter Bericht der Corn. 

Deutschen Meere, II. Abt. years 77-81. 

1884. Geo. Brook. Prelim. Acct. of Devel. of Lesser Weever-fish, Trachinus vipera, Linn. 

Jour., vol. xviii. 

1885. Geo. Brook. Devel. of Motella mustela, Linn. Soc. Jour., vol. xviii. 
1885. J. T. Cunningham. Significance of Kupffer's Vesicle, &c, Quart. Jour. Micr. Sci. 
1885. J. T. Cunningham. Relations of Yolk to Gastrula in Teleosteans, Ibid. 



1881. JonN A. Ryder. 

1881. John A. Ryder. 

1882. Jon.\ A. Ryder. 

1883. John A. Ryder. 

1884. John A. Ryder. 
1878. 



1SS4. 



Unt. 



Soc. 



EGGS AND LARV^l OF TELEOSTEANS. 135 

1 885. Miecz v. Kowalewski. Furch. und Keimblatteranlage der Teleostier, S. B. der physik. medicin. 

Societal, Erlangen, 1 5th. Dec. 

1886. Miecz v. Kowalewski. Ueber die ersten EntwickL processe der Knochenfische, Z. f. wiss. 

Zool., Bd. xliii. 
1886. Miecz v. Kowalewski. Gastrulation und Allantois bei den Teleostiern, S. B. d. phys. med. 

Societat, Erlangen, June 7. 
1880. Carlo Emery. Fauna and Flora des Golfes von Neapel.— IF e . Monographie, Fierasfer. 
1880. A. C. Gunther. Art. "Ichthyology," Ency. Britannica. 
1880. A. C. Gunther. Introduction to Study of Fishes, Edinburgh. 
1880-84. Francis Day. British Fishes, London and Edinburgh. 



DESCRIPTION OF PLATES. 
Plate I. 

Fig. 1. Egg of herring towards the close of period of simple segmentation, 11 hours after fertilisation. 

Aug. 26, 1884. Zeiss A, Oc 3. 
Fi"'. 2. Anterior end of herring embryo, 6 days after fertilisation, 1 day before hatching. Sept. 1, 

1884. Zeiss A, Oc 3. 
Fig. 3. Herring larva nearly 24 hours after hatching. Aug. 22, 1884. Zeiss A, Oc 2. 
Fig. 4. Outline of alevin of Salmo levenensis, 3 days after hatching. Magnified about 4 times. 
Fig. 5. Ovum of Osmerus eperlanus, Lacep, 25 J hours after fertilisation. May 7, 1886. Mag. 

33 times. 
Fig. 6. Ovum of Os. eperlanus : optical section through suspensory membrane, internal zona, and 

micropyle. Zeiss CC, Oc 2. 

Plate II. 

Fig. 1. Embryo of Pleuronedes platessa, Linn., in ovo, 23 days 5 hours after fertilisation. Mag. 33 
times. Feb. 26, 1886. 

Fig. 2. Sculpturing of surface of vitelline membrane of ovum of PI. platessa, L. Mag. 50 times. 

Fig. 3. Larva of PL platessa, taken artificially from ovum on point of hatching. 27 days after fertili- 
sation. Mag. 33 times. 

Fig. 4. Ovum of PI. flesus, 2 days 2J hours after fertilisation. Mag. 33 times. The development of 
this egg was retarded : end of the period of simple segmentation. 

Fig. 5. PL flesus, 22 hours after fertilisation, stage just before appearance of segmentation cavity. 
Mag. 33 times. March 31, 1886. 

Fig. 6. PL flesus, 2 days 2J hours. First appearance of segmentation cavity. Mag. 33 times. 

Fig. 7. PL flesus, 2 days 22 hours. Mag. 33 times. 

Fig. 8. PL flesus, newly hatched. 7 days. April 6, 1886. Pigment black, anus open. Mag. 33 times. 

Fig. 9. Ovum of Pleuronedes limanda, L., 20J hours after fertilisation. Stage preceding formation of 
segmentation cavity. May 22, 1886. Mag. 33 times. 

Fig. 10. Blastoderm of unfertilised ovum of PL limanda, showing expulsion of polar globule. 

Fig. 11. Spermatozoon of PL limanda. Zeiss DD, Oc 4. 

Plate III. 

Fig. 1. Newly shed unimpregnated ovum of PL limanda, optical section showing micropyle and rela- 
tions of protoplasmic layer. Zeiss A, Oc 3, Abbe's camera. Mag. 70 times. 

Fig. 2. PL limanda, J hour after fertilisation. Zeiss A, Oc 3, camera. Mag. 70 times. 

Fig. 3. PL limanda, 1-|- hours after fertilisation. Mag. 70 times. 

Fig. 4. PL limanda, 3 hours after fertilisation. Mag. 70 times. 

Fig. 5. PL limanda, little more than 3 hours : process of first division. Mag. 70 times. 

Fig. 6. PL limanda, larra newly hatched. May 28, 1886. Mag. 33 times. 

Fig. 6a. Notochord of same. Zeiss CC, Oc 3. 

Fig. 7. Blastodisc of PL cynoglossus, unfertilised 2 hours after shedding, shows what may be the 
second polar body. Mag. 70 times. 



136 ME J. T. CUNNINGHAM ON THE EGGS AND LARV^I, ETC. 

Fig. 8. Ovum of PL cynoglossus, 2 hours after fertilisation. Mag. 33 times. 
Fig. 9. PI. cynoglossus, unfertilised, 6 hours after shedding. Mag. 33 times. 

Plate IV. 

Fig. 1. Blastoderm of PL cynoglossus in process of first division, 3| hours after fertilisation. Zeiss 

CC, Oc 3. 
Fig. 2. PI. cynoglossus, | hour after fertilisation, ovum treated with acetic acid and methyl green, and 

examined entire in glycerine ; optical section of hlastodisc ; shows male and female pronuclei. 

Zeiss CC, Oc 3, camera. 
Fig. 3. Blastoderm of PI. cynoglossus, immediately after first division : shows nucleus in each of the two 

cells. Acetic acid and methyl green. Zeiss Cc, Cc 2, without camera. 
Fig. 4. PL cynoglossus, 4-cell stage, 4 hours. Mag. 33 times. 
Fig. 5. Optical section of 4-cell blastoderm, acetic acid and methyl green : shows absence of periblast 

beneath blastoderm. Zeiss CC, Oc 2. 
Fig. 6. PL cynoglossus 8-cell stage dividing; acetic acid only without glycerine, 6 hours after fertilisation. 

Mag. 33 times. 
Fig. 7. PL cynoglossus, blastoderm commencing to spread, 24 hours. Mag. 33 times. 
Fig. 8. PL cynoglossus, segmentation cavity, 1 day 5 hours. Mag. 33 times. 
Fig. 9. PL cynoglossus, 1 day 8 hours. Mag. 33 times. 
Fig. 10. PL cynoglossus, 1 day 23| hours. Mag. 33 times. 
Fig. 11. PI. cynoglossus, 2 days 4 hours. Mag. 33 times. 
Fig. 12. PL cynoglossus, 2 days 19 hours. Mag. 33 times. 

Plate V. 

Fig. 1. PL cynoglossus, 2 days 19 hours. Mag. 33 times. 

Fig. 2. PL cynoglossus, 3 days 1J hour. Mag. 33 times. 

Fig. 3. PL cynoglossus, 4 days. Mag. 33 times. 

Fig. 4. Newly hatched larva of PL cynoglossus, 5 days. Mag. 33 times. 

Fig. 4a. Notochord of PL cynoglossus. 

Fig. 5. Condition of rectum, r, and coalesced ends of segmental ducts, s.cl., in newly-hatched larva. Zeiss 

CC, Oc 2. 
Fig. 6. Condition of same parts, 30 hours after hatching. 
Fig. 7. Larva of PL cynoglossus, 2 days after hatching. 

Plate VI. 

Fig. 1. Gci'lus ccglefinns, L., newly hatched. Mag. 33 times. 

Fig. 2. Adhesive ovum from shore near station, probably Coitus scorpini. Mag. 33 times. 

Fig. 3. Adhesive ovum attached to Hijdrallmannia falcata, perhaps Liparis Montagui. Mag. 33 times. 

Fig. 4. Young fish, 2 days after hatching. Hatched from adhesive ova taken in trawl April 29, 1884. 

Liparis Montagu!. 
Fig. 5. Ovum of Cyclopterus lumpus. Mag. 33 times. 

Plate VII. 

Fig. 1. Newly hatched larva of Cyclopterus lumpus, ventral surface, from specimen preserved in spirit. 

Mag. '•'>'■) times. 
Fig. 2. Pelagic ovum taken 10 miles E.S.E. of May Island, March 23, 1886. Mag. 33 times. 
Fig. 3. Pelagic ovum taken in Firth of Forth, off Gullane Ness, May 27, 1886. Mag. 33 times. 
Fig. 4. Larva newly hatched from ovum shown in previous figure. Mag. 33 times. 
Fig. 4a. Notochord of same. Zeiss CC, Oc 3. 

Fig. 5. Pelagic ovum taken off Gullane Ness, May 27, 1886. Mag. 33 times. 
Fig. 6. Larva newly hatched from same. Mag. 33 times. 
Fig. 7. Teleostean ova from Gulf of Guinea. Mag. 18 times. Species unknown. 



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"V. — On the Fructification of some Ferns from the Carboniferous Formation. 
By Eobert Kidston, F.R.S.E., F.G.S. (Plates VIII., IX.) 



CONTENTS. 



PAGE I PAGE 



Calymmatotlieca bifida, L, & H., sp., . 140 

Soroeladus antecedens, Kidston, . .143 

Calymmatotlieca affinis, L. & H., sp., . 145 

Calymmatotlieca asteroides, Lesqx., sp., . 148 



Zeilleria Avoldensis, Stur, sp., . . .148 
Neuropteris lieteropliylla, Brongt., . .150 
Alcicornopteris convolida, Kidston, . .152 



Calymmatotheca, Stur, emend. 
Kidston, Quart. Jour. Geol. Soc, vol. xl. p. 590. 

In a Review * of Dr Stur's Zur Morphologie unci Systematik der Culm- 
und Carbonfarne,\ I pointed out that he appears to have included two types of 
fern fructifications in his genus Calymmatotheca. 

The first type includes those forms originally placed in Calymmatotheca \ 
and consists of a number of exannulate sporangia arranged around a common 
point of attachment ; the second type, which was first described in Zur. Morph., 
u. Syst. d. Culm- u. Carbonfarne.^ is there represented by C. Avoldensis and C. 
Frenzli. The fruit of these two species is apparently surrounded by an involucre 
or indusium, and it is only with this part of the fructification that we are at 
present acquainted. I also further indicated that in Calymmatotheca, as I pro- 
posed to restrict the genus, the fruiting portions of the frond are entirely 
deprived of foliage pinnules, whereas in the other type (C. Avoldensis and C. 
Frenzli) only a very slight modification takes place in the fertile portion of the 
fronds — the sporangia being borne on the ordinary foliage pinnules. 

In a subsequent paper,|| when describing the fruit of Sphenopteris delicatida, 
Sternb., 1 more fully explained the structure of such frutifications as those 
occurring in C. Avoldensis and C. Frenzli, and for these three species 
proposed the new genus Zeilleria. 

* Geol. Mag., Dec. III. vol. i. p. 328, July 1884. 

f Sitzb. dei' k. Akad. der Wissensch., Band lxxxviii. 1 Abth., 1883. 

% " Culm-Flora," Heft ii. p. 255, Abhandl. d. k. k. geol. Reiclisanst, vol. viii. Of the four figures of 
Calymmatothecous fruits given here by Stur, C. Schimperi, C. minor, C. Haueri, and C. Stangeri, my 
interpretation of the structure of these fruits is chiefly founded on C. Stangeri, as this seems the most 
perfectly preserved. 

§ p. 799. || Quart. Jour. Geol. Soc, vol. xl. p. 590. 

VOL. XXXIII. PART I. S 



138 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

On the specimens of Z. delicatula, Sternb., sp., figured in the Quart. Jour. 
Geol. Soc, vol. xl. pi. xxv., the development of the fruit can be traced. It at 
first consists of a globular indusium, which at maturity splits into four valves 
for the dissemination of the spores. 

On the other hand, what I regard as the true interpretation of the fruit of 
Calymmatotheca is that which was first propounded by Renault * and more 
fully explained and illustrated by Zeiller, t viz., that in Calymmatotheca the 
fruit consists of a number of exannulate sporangia, arranged around a common 
point of attachment. 

In the case of C. (Sorocladus) aster oides, Lesqx.,j there can be no doubt 
that the component parts of this star-like fructification are sporangia, and not 
thong-like segments of a split involucre. 

In his last work, Die Carbon-Flora der Schatzlarer Schichten,§ Dr Stur 
freely criticises my remarks on his genus Calymmatotheca as employed by him 
in his Zur Morph. u. Syst, d. Culm- u. Carbonfarne, and still adheres to his 
original opinion that the portion of the fruit of Calymmatotheca with which we 
are acquainted, is the thong-like remains of a split indusium. He also mentions, 
in regard to his C. Stangeri, that he has observed in a few cases at the base of 
the beaker -like indusium, small convex elevations. 

Notwithstanding this, I still think that Dr Stur is mistaken in his interpre- 
tation of the fruit of Calymmatotheca, and that in C Stangeri the fruit consists 
of a number of sporangia arranged around a common axis, as in C. [Sorocladus) 
aster oides, Lesqx., C. {Sjrfieitojrteris) bifida, L. & H., and C. affinis, L. & H., sp., 
to be presently described. The small elevations at the base of the inner cavity 
of the indusium (?) of C Stangeri, to which Dr Stur again refers in his Carbon- 
Flora,^ have, I am afraid, no organic connection with the fruit, and are perhaps 
due to mineralisation or to the adhesion of some extraneous matter. I make 
this suggestion from an examination of the fruit of C. {Sphenopteris) bifida, 
L. & H., and C. {Sylienopteris) affinis, L. & H., which are similar in all external 
respects to Stur's Calymmatotheca; and as in these cases the fruit is certainly 
not composed of thong-like segments of a split indusium, but of true exannulate 
sporangia, I am induced to believe that Dr Stur, through imperfect preserva- 
tion of his specimens, is mistaken in their interpretation. 

* Cows d. Botan. Foss., Troisieme Aunee, p. 198, 1883. 

f Ann. d. Scienc. Nat., 6 e s6r. Bot., tome xvi. p. 182, pi. ix. figs. 10, 11. 

% Lesquereux, Rf.pt. Geol. Survey of Illin., vol, iv. p. 406, pi. xiv. figs. 6, 7 ; Coed Flora of Pennsyl, 
p. 328, pi. xlviii. fig. 9; see also Zeiller, Ann. d. Scienc. Nat., loc. cit., p. 182, pi. ix. figs. 10, 11. 

§ Abhandl. d. 7c. Jc. geol. Reichsanst. , Band xi. Abth. 1, p. 239, Wien, 1885. It is to be regretted 
that Dr Stur here accuses M. Zeiller of writing anonymously my Review of his Carbon-Flora, contri- 
buted to the Geol. May., which communication M. Zeiller had neither seen nor was aware of, till after 
its publication — especially as the paper more fully explaining my views on this subject was published 
in the Quart. Jour. Geol. Soc, Aug. 1, 1884. 

|| Loc. cit., p. 238. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION". 139 

In regard to C. Haueri, Stur,* the type has apparently been so imperfectly 
preserved that little of its structure can be discerned — the specimen is repre- 
sented by little more than a mere carbonaceous stain on the matrix. It, 
however, shows the peculiar character of the sporangia (?) (segments of the 
indusium according to Dr Stub) being united in pairs by their basal por- 
tions, but whether the thong-like bodies are segments of a split indusium or 
sporangia cannot be satisfactorily settled from an examination of his figure. 
The union of the thong-like bodies in pairs is taken as an objection by Dr 
Stur to the sporangial explanation of these fruits, but as the union of 
sporangia is of frequent occurrence in the Marattiacew, their apparent 
partial union in C. Haueri does not militate against the view that in 
Calymmatotheca we are dealing with marattiaceous sporangia arranged in 
groups. 

As to the affinities of these ferns, I have nothing to add to that mentioned 
in my former paper in the Quart. Jour. Geo!, Soc, where I said, " Calymmato- 
theca as here restricted (and as restricted in the present communication) is 
probably related to the Marattiacece, whereas Zeilleria appears to have 
affinities with the Hymenophyllaceee."^ This is very different to that which Dr 
Stur gives as my views on the affinity of Calymmatotheca, where he states, 
" Dass Calymmotheca eine Hymenophyllacee, wie der ungenannte Autor meint, 
nicht sein konne, geht klar aus dem Fehlen des verlangerten oder fadenformigen 
Receptaculums am Grunde der Kapsel hervor."| 

It was only the members of the genus Zeilleria that I thought might have 
hymenophyllaceous affinities, but as none of the specimens of this genus, which 
have come under my notice, have afforded any glimpse of the arrangement of 
the spores within the indusium (whether they were attached to a column or not), 
we can only throw out a suggestion as to the affinities of Zeilleria, a suggestion 
which must be corroborated or refuted as subsequent investigations decide. 
Calymmatotheca, however, as I have proposed to restrict it, possesses appa- 
rently an undoubted marattiaceous form of fruit. 

The specimens to which reference was made when first treating of Dr Stur's 
genus Calymmatotheca were those on which the genus Zeilleria, were founded,§ 
hence Dr Stur is mistaken in assuming that my views were established on a 
Hawlea. 

A further distinction that was pointed out between Calymmatotheca and 
Zeilleria is found in the fruiting portions of the fronds of Calymmatotheca being 
reduced to masses of fruit, unassociatecl with any ordinary foliage pinnules, 
whereas in Zeilleria the fruiting portion of the frond varies little from the 
ordinary barren condition, the fertile being mixed with the ordinary barren 

* Culm-Flora, Heft i. pi. i. fig. 2. f Quart. Jour. Geol, Soc, vol. xl. p. 591. 

X Carlon-Flora, p. 241. § Quart. Jour. Geol. Soc, vol. xl. p. 590. 



140 ME ROBERT KIDSTON ON THE FRUCTIFICATION OF 

pinnules. This condition is said by Dr Stur to occur in his C. Schatzlariensis* 
but the figures of this species given on his pi. xxxviii. are very imperfect, and 
little can be learnt of the fruit from them ; and from the meagre evidence 
afforded by the woodcut on p. 238, one would not like to say definitely whether 
this fern should be referred to Calymmatotlieca or ZeilleriaA 



Calymmatotlieca bifida, L. & H., sp. 
PI. VIII. figs. 1, 2, 3, 4, 5, 6a; PI. IX. figs. 16, 17. 

Calymmatotlieca bifida, Kidston, Quart. Jour. Geol. Soc, vol. xl. p. 591 (foot-note). 

Sphenopteris bifida, Liudley and Hutton, Fossil Flora, vol. i. pi. liii. 

Sphenopteris bifida, Hibbert, Trans. Roy. Soc. Edin., vol. xiii. p. 177, pi. vi. figs. 1, 2. 

Sphenopteris bifida, Kidston, Trans. Roy. Soc. Edin., vol. xxx. p. 537. 

Sphenopteris bifida, Miller, Testimony of the Rods, Edin., 1857, p. 466, fig. 129. 

Trichomanites bifidus, Goppert, Syst. fil. foss., p. 264, pi. xv. fig. 11. 

Todea Lipoldi, Stur, Cuba Flora, Heft. i. p. 71, pi. xi. fig. 8; Heft. ii. p. 291. 

Todea Lipoldi, Scbimper in Zittel, Handbuch der Paleontologie, Band ii. Heft. i. p. 107, fig. 75. 

Sphenopteris friyida, Heer, Foss. Flora Spitzbergens,% p. 6, pi. i. figs. 1, 3-6. 

(T) Sphenopteris geniculata, Heer, Foss. Flora Spitzbergens, p. 7, pi. i. figs. 8 and 10 (1 7 and 9). 

Spheyiopteris rutazfolia, Schmalhausen (not Gutbier), Mem. de la Acad. Imper. d. Sciences de Si 

Petersbourg, vii e s<$r. vol. xxxi. No. 13, p. 4, pi. i. figs. 1-4 (1 fig. 5), 1883. 
Stap)ltylopteris Pcachii, Kidston (not Balfour), Trans. Roy. Soc. Edin., vol. xxx. p. 539, pi. xxxi. 

fig. 6. 
Sphenopteris {Diplothmema) tracyana, Lesquereux, Coal Flora of Pennsyl., vol. iii. p. 766, pi. ci. 

fig. 2, 1884. 

Description, — Frond divided into two symmetrical lanceolate portions by a 
dichotomy of the main axis. Pinnae sub-opposite or alternate, linear; pinnules 
sub-opposite, or alternate and divided into 3-8 simple or bifid, narrow, linear, 
single-nerved segments. Fruiting pinnae deprived of foliage pinnules, and 
borne on the main rachis in the neighbourhood of the bifurcation. Fruit 
consisting of about 16-20 linear sporangia arranged in a circle around a 
common axis, and situated at the extremities of the bifurcations of the fruiting 
pinnae. Sporangia free in their upper portion, but united below. 

Remarks. — The type specimen of this species, figured by Lindley and 
Huttox, gives a very unsatisfactory idea of the true form of this fern, their 
example having evidently suffered so much from maceration before fossilisation 
took place, that the delicate limb of the pinnule has entirely decayed, the veins 
only remaining. 

A much more characteristic figure than 'that given by the authors of the 

* Die Carbon-Flora, p. 265, pi. xxxviii. figs. 1, 2. 

f It is unfortunate that many of tbe figures on the plates of Dr Stur's Carbon-Flora are so 
indistinct that it is quite impossible to discuss minute details of structure from them. 

X Kongl. Svenska Vetenslcaps-Akadcmiens Ilandlingar, Band xiv. No. 5, Stockholm, 1876. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 141 

Fossil Flora, is the small woodcut given by the late Hugh Miller in the 
Testimony of the Rocks. This example is refigured on PI. IX. fig. 16. Another 
figure, showing well the form of the pinnae and pinnules of C. bifida, is given 
by Stur in his Culm Flora, under the name of Toclea Lipoldi. The pinnules are 
divided into 3-7 very narrow linear segments, in each of which is a simple central 
vein. The limb of the pinnule is very narrow, forming only a slight border 
to the nerve. 

On PI. VIII. fig. 1, the specimen has so suffered from decay, that nothing of 
the pinnules now remains but the veins, the specimen being in fact reduced to 
the same state of imperfection as that of Lindley and Hutton's original type of 
the species. This example, however, is specially interesting, as it shows the posi- 
tion of the fruit on the frond, which is here seen to be situated in the neighbour- 
hood of the bifurcation of the main axis. From the specimen drawn at fig. 2, it 
is shown that in the fruiting pinnae the synangia are borne at the extremities 
of the little branches resulting from a third or fourth series of dichotomies. 

On the surface of the sporangia are generally seen, in well-preserved 
examples, a few longitudinal fine ridges. At figs. 6a and 3a, two of the 
synangia are exhibited in profile. At fig. 4, and also in figs. 2 and 3, are 
represented flattened out groups of sporangia. 

The sporangia individually are slightly fusiform, and united in their basal 
portion.* 

The affinities of this fern seem to be undoubtedly with the Marattiacew, 
and in the genus Kaulfussia the sporangia are united to each other round a 
common point, an arrangement with which the fruit of C. bifida closely 
corresponds. 

In C. bifida the synangia differ from those of Kaulfussia in the sporangia 
being free for a considerable portion of their length and in the position of 
the synangia on the fern. In Kaulfussia the synangia are scattered on the 
back of the frond. In the more essential structural characters of the fruit, 
however, the close analogy between the fruit of C. bifida and Kaulfussia is 
very striking. 

Specimens showing the bifurcation of the rachis are not uncommon, and on 
the main axis below the bifurcation there are a few barren pinnae, which are 
usually much smaller and less divided than those above the bifurcation. The 
pinnae within the fork, formed by the dichotomy of the axis, are at the base of 
the two arms much shorter than those on the outer side of the fork, but they 
gradually increase in size as the arms of the fork separate from each other. 
The fronds never seem to have attained to large dimensions. 

* In one or two sporangia I think there can he detected a small elongated pore a little below the 
apex, but defer positively affirming its presence till I have more frequently seen its occurrence, and so 
convince myself that this appearance is not accidental. 



142 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

The sporangia of C. bifida are more numerous, narrower, and slightly larger 
than those of C. affinis, L. & H., sp., to which I in error referred the first 
specimens of the fruit of C. bifida* 

Sph.frigida, Heer, and Sph. geniculata, Heer, seem to have been founded on 
imperfectly preserved fragments of C. bifida, L. & H., sp. 

To C. bifida must also I think be referred S. rutwfolia, Schmalhausen 
(not Gutbeir) and S. tracyana, Lesquereux. Any one having only the 
original figure of Ltndley and Hutton to guide them in their identification 
of this species, may be very well excused for regarding Todea Lipoldi, Sph. 
rutwfolia, Schmalhausen, and S. tracyana, as specifically distinct from C. 
bifida; but from the examination of numerous specimens, many of which 
came from the original locality, I have no doubt that all the names 
included in the list of synonymy here given under C. bifida refer to this one 
species. 

Description of Specimens. — Fig. 1. This specimen was collected by Mr 
John Jackson on the River Irthing, within a mile above Lampert, and 
communicated to me by Mr Hugh Miller, F.G.S. The specimen is 
badly preserved, and reduced very much to the same condition as that 
of the original type figured by Lindley and Hutton in their Fossil Flora, 
pi. liii., where the limb of the pinnules has entirely disappeared, leaving only 
the veins. Notwithstanding, however, the imperfect state of the example 
shown at fig. 1, it is interesting, as distinctly showing the position occupied 
by the fructification of this species, which is on the rachis below the dichotomy 
as well as on the base of the two arms of the fork. 

Specimen from Lewis Burn, rather over 200 yards below Lewis Burn Colliery, 
N. Tynedale, Northumberland (fig. 2), in the Collection of the Geological 
Survey of England, collected by Mr J. Rhodes. This example, which occurs 
in association with barren fragments of C. bifida, exhibits the characteristic 
dichotomisation of the fructifying branches of this species, and in fact of the 
genus Calymmatotheca. The rachis of the pinnae here seems to undergo three 
series of dichotomies, at the extremities of the ultimate forks of which the 
synangia were borne, f 

Specimen from Back Burn, ojDposite Cranecleuch New Houses, N. Tynedale, 
Northumberland, collected by Mr J. Rhodes, in the Collection of the Geological 
Survey of England (fig. 3). The specimen figured lies on the corner of a 
small slab which contains a great many groups of the sporangia of this 
species. These groups seem to be much crushed and flattened out, 
and little of the intimate structure is discernible. Only slight traces of 
the stem which bore the synangia is preserved in this example. The 



r 



Trans. Roy. Sor. Edin., vol. xxx. p. 539, pi. xxxi. fig. 6 



t See Trans. Roy. Soc. Edin., vol. xxx. pi. xxxi. fig. 6. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 143 

synangium, lettered a, shows very clearly the union of the sporangia in their 
lower portions. 

Specimen from Bateinghope Burn, Redesdale, Northumberland (figs. 4 and 
5a). This small example shows four synangia, lettered respectively a, b, c, d, of 
which a and b are the two most perfect. Each synangium appears to contain from 
18-20 sporangia. For about half their length the sporangia are free, but their 
basal portions are united. The individual sporangia, though now compressed, 
show a distinct rotundity, and have usually one or two well-marked longi- 
tudinal ridges. The sporangia must have originally possessed considerable 
substance, for in the fossil state they are frequently converted into a coaly 
material, which, from its brittle nature, when the stones containing the fossils 
are split, commonly causes the free portions of the sporangia to spring from 
the matrix, only leaving their impressions on the stone. 

Specimen from Lewis Burn, over 200 yards below Lewis Burn Colliery, N. 
Tynedale, Northumberland (fig. 6), collected by Mr J. Bhodes, in the Collection 
of the Geological Survey of England. This small slab shows two different types 
of fern fructification lying side by side. That marked a is a synangium of 
C. bifida, but the other is evidently the remains of an indusium split into five 
segments. Unfortunately, very few fragments of this interesting fern fructifi- 
cation (Qb) have been discovered ; but another, though imperfect example, shows 
the indusia attached to a rachis in a somewhat similar manner to those of 
Sorocladus stellatus, Lesqx.* It differs, however, from that species in the 
larger size of the indusium, and in the frond being apparently bipinnate, at 
least the small fragment showing these fruits attached to the rachis exhibits a 
bipinnate disposition of the indusia. I propose provisionally to designate this 
species as Sorocladus antecedens. The plant I here place in Sorocladus differs 
from Zeilleria in the fruiting portion being altogether destitute of ordinary foliage 
pinnules. The few fragments of this species which have been collected come 
from the same locality. 

Specimen from Burdiehouse, Mid-Lothian, in the " Hugh Miller Collec- 
tion," Museum of Science and Art, Edinburgh (PI. IX. figs. 16 and 17). This 
example, which is the original of the small woodcut given by Hugh Miller 
in the Testimony of the Rocks, Edinburgh, 1857, p. 466, fig. 129, is reproduced 
here natural size. It shows one of the two main divisions of the frond, and 
bears about 22 pairs of opposite pinnae. The pinnae on the right of the figure 
are longer than those on the left, the latter having been situated within the 
fork of the frond. 

The pinnae are lanceolate, the longer ones bearing about 14 pairs of 
pinnules, which vary from simple to being divided into 8 linear, single-nerved, 
simple, or bifid segments, according to their position on the pinnae. The 

* Coal Flora of Pennsyl, p. 328, pi. xlviii. fig. 8. 



144 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

pinnules towards the centre of the pinnae are longest. The pinnules of the 
superior side of the pinnae are longer than those on its inferior side. 
Figs. 17, a, b, c, show some of the pinnules slightly enlarged. 

There is another example from Burdiehouse in the " Hugh Miller Collec- 
tion," Museum of Science and Art, Edinburgh, which is interesting as showing 
very beautifully the bifurcation of the main axis, below which, as well as on 
the two arms of the fork, the frond bears barren pinnae. It further shows 
that the pinnae within the fork are shorter than those attached to the outer 
side of the fork, a character well shown in fig. 16. 

Several specimens, also showing the bifurcation of the main axis, are 
contained in the Collection of the Geological Survey of Great Britain. 

My thanks are due to Dr Traquair, keeper of the Natural History Depart- 
ment, Museum of Science and Art, Edinburgh, for permission to figure the 
specimen shown on PL IX. fig. 16. 

Horizon. — Calciferous Sandstone Series. 

Localities : — 

Scotland. — Burdiehouse, near Edinburgh ; Muir Burn, Kershope Burn, and 
Tweeden Burn, Liddesdale ;* and River Esk, Glencartholm, Eskdale. # 

England — Northumberland. — Shore section, Sandstone Quarry, a little 
south of Sea Houses; Bateinghope Burn, 1 mile from head of stream, Redesdale; 
east bank of Lewis Burn, Barney's Cut, a little more than ^ mile south-west 
of Lewis Burn Bridge, North Tynedale ; Lewis Burn, more than 200 yards 
below Lewis Burn Colliery, North Tynedale; Buck Burn, f mile north-west of 
Willow Bog, Oakenshaw Burn, North Tynedale ; Cranecleuch Burn, opposite 
Cranccleuch New Houses, Whickhope Burn, North Tynedale ; foot of Sauchy 
Sike, Little Whickhope Burn, North Tynedale; Rigend Burn, Kielder, N. 
Tynedale. Cumberland. — River Irthing, \ mile north of Lampert (county 
boundary, Northumberland and Cumberland); foot of streamlet, f mile south- 
west of Wileysike, River Irthing ; River Irthing, 2 miles north-east of Water- 
head ; River Irthing, £ mile east of Waterhead ; Bothrigg Burn, near its head, 
1 mile east of the Flat, Bewcastle; stream between Oakshaw and Whinting- 
stone, Clattering Ford, Bewcastle.t 

* Collected by Mr A. Macconchie, Fossil Collector to the Geol. Sur. of Scotland. 
f The specimens from Northumberland and Cumberland have been mostly collected by Mr J. 
Rhodes, Fossil Collector to the Geol. Sur. of England. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 145 

Calymmatotheca affinis, L. & H., sp. 
Plate IX. figs. 18-22. 

Calymmatotheca affinis, Kidston, Catalogue of Palceoz. Plants in Brit. Mus., p. 66, 1886. 
Sphenopteris affinis, Lindley and Hutton, Foss. Flora, vol. i. pi. xlv. 

Sphenopteris affinis, Hibbert, Trans. Roy. Soc. Edin., vol. xiii. p. 178, pi. vi. fig. 4; PI. v. lis. 
Sphenopteris affinis, Peacb, Quart. Jour. Geol. Soc, vol. xxxiv. p. 131, pi. vii. 
Sphenopteris affinis, Peacb, Trans. Bot. Soc. Edin., vol. xii. pp. 162 and 187. 
Sphenopteris linearis, Brongniart (not Sternberg), Hist. d. veget. foss., p. 175, pi. liv. fig. 1. 
Sphenopteris linearis, Hibbert, Trans. Roy. Soc. Edin., vol. xiii. p. 178, pi. vi. fig. 3. 
Staphylopteris (?) Peachii, Peach, Quart. Jour. Geol. Soc, vol. xxxiv. p. 131, pi. viii. 

figs. 1,2, 3(4?). 
Sphenopteris frigida, Heer (in part) Foss. Flora Spitzbergens, pi. i. fig. 2. 
Sphenopteris flexilis, Heer (in part), Foss. Flora Spitzbergens, p. 8, pi. i. figs. 11-27 (pi. ii. 

figs. 7-10?) 

Description. — Frond divided into two symmetrical, lanceolate parts, tri- 
pinnate or decompound ; primary pinnae alternate, lanceolate ; secondary and 
tertiary pinnae alternate and broadly lanceolate ; pinnules cuneate, entire or 
divided into 2-3 cuneate lobes. Veins numerous, radiating from the base of 
the pinnule, and dichotomising 2-3 times. Fructification consisting of 4-6 
oblong exannulate sporangia borne at the extremities of the dichotomously 
divided fertile pinnae, which are wholly deprived of foliage pinnules. Position 
of fertile pinnae not yet observed, but probably holding the same position on the 
frond as those of Calymmatotheca bifida. Rachis smooth. 

Remarks. — The plant figured by Brongniart as Sphenopteris linearis is 
evidently not Sternberg's fern of that name.* The specimen that has served 
as the type of Sternberg's Sph. linearis is so imperfect that, from any evidence 
afforded by the figure, it is very improbable it will ever be known what his fern 
really is. 

On the other hand, the plant figured by Brongniart as Sph. linearis is the 
same as that earlier described by Lindley and Hutton as Sph. affinis. The 
type figure of Sph. affinis is unfortunately not very characteristic of the species, 
and though small pinnuled forms occur, the pinnules are always more cuneate 
than shown in the figure given on plate xlv. (vol. i.) of the Foss. Flora. As 
far as this character is concerned, the figure given by Brongniart is more 
satisfactory, but perhaps the most characteristic figures are those given by 

HlBBERT.t 

It may be added that the specimen figured by Lindley and Hutton as Sph. 
UnearisX which is fortunately preserved in the Hutton Collection (Museum of 
Natural History, Newcastle-on-Tyne), is not the Sph. linearis, Bgt. ( = Sph. 

* Sternberg, Vers. ii. p. 15, pi. xiii. fig. 4. f Trans. Roy. Soc. Edin., loc cit. 

X Foss. Flora, vol. iii. pi. ccxxx. 
VOL XXXIII. PART I. T 



146 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

affinis, L. & H.), but a fine specimen of the upper portion of Sph. crassa, L. & H. 
Their plate is not a satisfactory rendering of the fossil.* 

C. affinis, in the dichotomisation of the main axis and the general distribu- 
tion of the primary pinnae on the two forks of the dichotomy, follows the same 
arrangement as that occurring in C. bifida, L. & H., sp. 

Specimens of the fruit of C. affinis were first exhibited by the late Mr 
C. W. Peach at the meeting of the Bot. Soc. Edin., May 1874.t These were 
subsequently named Staphylopteris (?) Peachii by the late Prof. Balfour. 
Later Mr C. W. Peach found the Staphylopteris (?) Peachii united to Sphen- 
opteris affinis,\ but regarded it as a parasite. The structure, however, of 
Staphylopteris (?) Peachii, being that of a marattiaceous fructification, inde- 
pendently of the fact of a similar structure having been found organically 
attached to C. bifida in such a manner as to conclusively prove it is the fruit 
of that species, shows beyond all doubt that Staphylopteris (?) Peachii is the 
fruit of Sphenopteris affinis, and not a parasite. 

Mr C. W. Peach communicated a paper to the Geol. Soc. London on 
Sph. affinis and Staphylopteris (?) Peachii^ in which he figured some small 
specimens of the latter fossil. || 

In the same communication he describes and figures what he believed 
to be the true fruit of Sph. affinis.*^ The specimen from which this figure 
was taken was kindly shown me by its describer, but I could not distinguish 
other than some sand-grains or other inorganic matter adhering to the 
pinnules, which had been mistaken by my friend for fruit. I believe this view 
of the supposed fruit is that accepted by others who have seen the specimen. 

A very good restoration of the complete frond of C. affinis is given by 
Hugh Miller as a frontispiece to his Testimony of the Rocks. 

The figures of Sj)h. frigida and Sph. fiexilis, mentioned in the synonymy, 
appear to belong to this species. 

Description of Specimens. — Fig. 18. From Burdiehouse, near Edinburgh. 
This specimen, which is preserved in a dark grey limestone, shows the general 
form of the fern. The pinnae are lanceolate, the secondary pinnae being some- 
what more broadly lanceolate than the primary. The tertiary pinnae bear 2-4 
cuneate pinnules, which are either simple or compounded of 2-3 cuneate lobes. 
The veins are indistinctly preserved, the carbon of the plant being converted 
into a bright coal-like substance. 

Fig. 19. From Harwood Burn, below Limefield House, near West Calder, 
Mid-Lothian, in the Collection of the Geological Survey of Scotland. 

* See Kidston, Proc. Roy. Phys. Soc. Edin., vol. vii. p. 238. 

t Trans. Bot. Soc. Edin., vol. xii. p. 162. \ Trans. Bot. Soc, loc. cit., p. 187. 

§ Quart. Jour. Geol. Soc, vol. xxxiv. p. 131. || PI. viii. figs. 1-3 (4?). 

IT PI. vii. fig. 2. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 147 

Fig. 19b shows one of the pinnae of a large pinnuled form of C. affinis. 
This example, in the size of the pinnules, corresponds to Brongniart's Sphen- 
opteris linearis* The nervation is beautifully preserved, and is shown in the 
enlarged drawing, fig. 19#. 

Fig. 20. From West Calder, collected by the late Mr C. W. Peach. This 
sketch shows one of the largest fertile pinnae of C. affinis with which I 
have met. The pinna is destitute of foliage pinnules, and ramifies by a series 
of dichotomies. At a are shown the ultimate branchlets, but the synangia 
have become detached from their parent stalks, a few of which, however, are 
seen at a and b. These consist of 4-5 sporangia. 

Figs. 21-22 are copied from the plate which accompanies Mr C. W. Peach's 
paper in the Quart. Jour. Geol. Soc, vol. xxxiv. p. 131. Fig. 21 shows the 
synangia attached to their supporting pedicels, and fig. 22 gives a single 
synangium, which is enlarged at fig. 226 to show the five exannulate sporangia 
of which it is composed. 

Horizon. — Hitherto only found in the Calciferous Sandstone series, where 
in some localities it is plentiful. 

Localities : — 

Scotland — Berwickshire. — Bilsdean Creek, 1^ miles west of Cockburnspath 
(J. Bennie) ; Shore, west of Harbour, Cove, Cockburnspath (J. Bennie). 
Fifeshire. — Rocks above Kinghorn ; Flisk Quarry, St Andrews ; Grange 
Quarry, Burntisland ; Kilmundy Limestone Quarry, Burntisland (J. Bennie) ; 
Kilmundy Sandstone Quarry, Burntisland (J. Bennie) ; Dodhead Quarry, 
Burntisland (J. Bennie) ; east side of the Binn near Burntisland (J. Bennie) ; 
Brosyhall Lime Quarry, east of Burntisland (J. Bennie) ; Binnend Shale 
Works, Burntisland (J. Bennie). Haddingtonshire. — Long Craigs Bay, \\ 
miles west of Dunbar (J. Bennie). Buteshire. — Island of Arran (British 
Museum). Dumfriesshire. — Docken Beck, near Langholm (A. Macconochie) ; 
Glencartholm, Eskdale (A. Macconochie) ; Tinnis Burn, near Newcastleton, 
Liddesdale (A. Macconochie). Linlithgowshire. — Railway Cutting, Dalmeny 
Railway Station ; Dalmeny Shore, halfway between Long Craig and 
Newhall Piers, Queensferry (J. Bennie). Mid-Lothian. — Raw Camps, Mid- 
Calder [Fruit) ; Straiton Oil Works, near Loanhead ; Queen's Park, Edin- 
burgh (Professor Ross) ; Craigleith Quarry, near Edinburgh ; Lochend, Edin- 
burgh ; Addiewell ; Water of. Leith, below Red hall Mill Dam; Hailes 
Quarry, Kingsknowe, near Slateford (Professor D'Arcy Thomson), (Fruit), 
(T. Stock) ; Burdiehouse ; Banks of the Almond, Cramond (R. F. B. Bishop) ; 
Suburban Railway Cutting, Edinburgh (J. Gaul) ; West Hermancl, near West 
Calder (Fruit), (C. W. Peach) ; Harwood Burn, below Limefield House, near 
West Calder (J. Bennie) ; Currie (Fruit), (J. Bennie) ; Slateford; Shore at 

* Loc. cit., pi. liv. fig. 1. 



148 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

Wardie, near Granton (C. W. Peach) ; Inchkeith, Frith of Forth (J. 
Gaul). 

England — Cumberland. — Bull Cleuch, Kirk Beck, Bewcastle (H. Miller). 
Northumberland. — Warksburn, North Tynedale (H. Miller). 



Calymmatotheca aster oides, Lesqx., sp. 

Calymmatotheca aster oides, Zeiller, Ann. des Scienc. not., 6 e ser. Bot., vol. xvi. p. 182, pi. ix. 

figs. 10, 11. 
Stapliylopteris asteroides, Lesquereux, Report Geol. Survey of Illin., vol. iv. p. 406, pi. xiv. 

figs. 6, 7; Schimper, Traite d. paleont. veget., vol. iii. p. 512. 
Sorocladus asteroides, Lesquereux, Coal Flora of Pennsyl., p. 328, pi. xlviii. figs. 9, 9b. 

Remarks. — Among many other specimens of fossil plants contained in the 
collection of the late William Henry Johnson, Dudley, I observed two small 
specimens of this species. 

Unfortunately, they are not very well preserved, and do not add any additional 
information to the knowledge of the species. The general growth of the species 
is well shown in Lesquereux's figures, and their more minute structural details 
have been illustrated by Zeiller. The fructification consists of a number of 
elongated sporangia, usually six in number, arranged in a stellate manner 
around a common point of attachment. It is not yet known to which 
fern this fructification belongs, as the fertile portion shows no traces of the 
barren pinnules. 

Horizon. — Middle Coal Measures. 

Locality. — Coseley, near Dudley. 



Zeilleria Avoldensis, Stur, sp. 
Plate VIII. figs. 8-10. 

Zeilleria Avoldensis, Kidston, Quart. Jour. Geol. Soc, vol. xl. p. 591, 1884. 

Calymmotheca Avoldensis, Stur, "Morph. u. Syst. d. Culm. u. Carbonfarne," Sitzb. d. h. Alcad. d. 

Wissensch., vol. lxxxviii. p. 171, fig. 37. 

Die Carbon-Flora d. Scbatzlarer Schichteu, Abhandl. d. Jc. h. geol. Reichsanst., vol. xi. 
Abth. i. p. 251, pi. xxxviii. fig. 1, text fig. 41 on p. 238. 

Description. — Frond decompound (4-5 pinnate) ; primary pinnae broadly 
lanceolate, secondary pinnae lanceolate, and composed of about twenty pairs of 
tertiary pinnae. The tertiary pinnae are more or less lanceolate, but vary in 
outline according to their position on the frond. Pinnules attached to the 
rachis by their whole base and united among themselves, the free portion of the 
limb is ovate-triangular ; medial nerve clearly defined, and giving off 2-4 simple 
lateral branchlets, all of which extend to the margin of the pinnule. Fruiting 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 149 

portion of the frond confined to the lower secondary pinnae, where the fertile 
pinnules bear 1-3 pedicellate indusia at the extremities of the excurrent veins. 
In the earlier condition the indusia are oval, but at maturity split into four 
valves. 

Remarks. — From the figure of this species given by Dr Stur in his Carbon 
Flora, the fronds of this fern must have attained to large dimensions. The 
form of the tertiary pinnae varies much on the upper and lower parts of the 
fern ; on the upper portion they are small, about 3 mm. long, 2 mm. broad, and 
more or less oval in outline ; those towards the apex of the secondary pinnae 
are more or less united among themselves. On the lower secondary pinnae the 
tertiary pinnae are 15-20 mm. or more long, and bear many pairs of alternate 
pinnules, which are usually united to each other for ^ or § of their length. The 
free portion is triangular, and has a well-defined central and usually two 
lateral veins, one given off from each side of the medial nerve. The fertile 
pinnules do not differ in form from the barren, except in the veins being pro- 
duced to form little pedicels to which the oval indusia are attached (PI. VIII. 
figs. 9, 10). Occasionally only the upper pinnules are fertile, but quite as 
frequently the lower, as well as the upper pinnules bear fruit. 

The fruit of this fern, as pointed out by Dr Stur,'" is composed of four 
valves. This four-cleft appearance, however, is only shown when the indusium 
has reached maturity and split for the dissemination of the spores ; in the 
young state the indusia are oval as seen at PI. VIII. fig. 9. As to the manner 
in which the spores are arranged within the indusium nothing is known. 

Description of Specimen. — PI. VIII. fig. 8. The example figured is the 
only British specimen of this species with which I have yet met. It shows a 
portion of a secondary pinnae, bearing the remains of twelve tertiary pinnae, 
none of which are very complete, but all are fertile, except the two upper 
pairs. The fertile pinnules bear in some cases three (fig. 10) and in others 
only one indusium (fig. 9). 

At fig. 9 is exhibited the young, and at fig. 10 the more advanced con- 
dition of the indusia, where they have split into valves. 

This specimen was in the collection of the late Mr Henry Johnson, F.G.S., 
Dudley, from whom I received it for examination. 

Horizon. — Middle Coal Measures. 

Locality. — Corseley, near Dudley. 

* Carbon Flora, fyc, p. 254. 



150 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

Neuropteris heterophylla, Brongniart. 
Plate VIII. fig. 7. 

Neuropteris heterophylla, Brongniart, "Classification desVeg^taux Fossiles," Extract from Memoires 
du Museum cV histoire naturelle, tome viii. p. 33, pi. ii. fig. 6, 1822. 
Hist. d. Vegctaux Fossiles, p. 243, pi. lxxi. and pi. lxxii. fig. 2, 1828. 

Neuropteris Loshii, Brongniart, Hist. d. VegHaux Fossiles, p. 242, pi. lxxii. fig. 1, and pi. lxxiii. 
1828. 

Several authors have described what they believe was the fructification of 
the genus Neuropteris, Brongniart, but in all these cases the supposed fruit was 
either a parasitic fungus, or the fern bearing the fruit described had been 
referred to the genus Neuropteris in error. 

As early as 1826, Hoffmann figured what he regarded as the fruit of his 
Neuropteris ovata.* This consisted of a single lanceolate pinnule, 3 cm. long 
and 1 cm. wide, whose basal extremity appears to me rather to lie under the 
stem which is supposed to have borne it than to be attached to it. The upper 
surface of this supposed fruiting pinnule shows an indistinct granulation. Its 
preservation is, however, so imperfect that it seems impossible to say that 
this supposed fruit belongs to N. ovata, or even to any other member of the 
genus Neuropteris. 

The next supposed fruit of Neuropteris was figured by Brongniart in his 
Hist. d. veget. foss., p. 239, plate lxv. figs. 3 and 3a, where certain linear 
swellings situated between the nerves are irregularly scattered over the upper 
surface of a pinnule of Neuropteris Jlexuosa. In a subsequent part of the same 
work, p. 326, Brongniart corrected this erroneous interpretation of these 
bodies, and refers them to parasitic fungi, a view which receives confirmation 
from the occurrence of similar organisms on ferns belonging to different recent 
genera. 

Almost conclusive evidence against these bodies being the fruit of ferns 
is further afforded by their occupying the tissue of the pinnules between the 
veins, whereas the fruit of ferns is situated on some part of their nervation. 

In 1880 Fontaine and White, in their Permian and Upper Carboniferous 
Flora, give a figure of N hirsuta,f showing what they believed to be its fructifica- 
tion, but again this supposed fruit appears to be only another of those parasitic 
fungi, and one which seems very closely related to the species affecting the 
specimen of N Jlexuosa described by Brongniart. The supposed sori figured by 

* " Uber die Pflanzcnreste des Kohlengebirgcs von Ibbenbiihren und vom Piesberge bei 
Osnabruck, " in Keferstein's Teuchland geognostisch-geologisch dargetsellt, vol. iv. p. 158, pi. i. figs. 
5-8, Weimar, 1826. His fig. 8 is the supposed fruiting pinnule. 

t " Second Gcol. Survey of Pennsylvania, Report of Progress P.P.," The Permian or Upper Carbon- 
iferous Flora of West Virginia and S.-W. Pennsylvania, p. 47, pi. viii. figs. 7, 8, Harrisburg, 1880. 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 151 

Fontaine and White are also stated to lie between the veins, a circumstance 
which is fatal to the view that these bodies are the fructification of their fern. 

Bunbury * had previously figured and described similar organisms on the 
pinnules of N. Scheuchzeri (N. cordata, Bunbury, not Brongniart),t and had 
rightly referred them to a disease of the parenchyma or a parasitic fungus. 

In the Carboniferous formation, fossil parasitical fungi occur not only on 
various spcies of ferns, but on other plants also, and have been figured and 
described by various writers.^ 

N. keterophylla, Brongt. (with which N. Loshii, Brongt., is now known to 
be synonymous), has also had its supposed fruit described by Gutbier in 1849, § 
but in this case, even if the bodies which were supposed by Gutbier to be the 
fruit of his fern really prove to be its fructification, we are still in ignorance 
of the fruit of Neuropteris, as Gutbier's fern does not belong to this genus, 
but to Odontopteris.\\ 

The specimen now described exhibits very clearly the mode and character 
of the growth of the fruiting portion of Neuropteris. It was discovered by 
Mr T. Stock, by whom it was communicated to me for examination. 

The fossil shows an axis a about 8 cm. long, which gives off apparently two 
pairs of lateral pinnae, b, c and d, e. The terminal portion of the specimen 
ends in a number of dichotomous branchlets, the ultimate divisions being 
about 8 mm. long, and bearing the fruit at their summits. On the terminal 
part of the fossil there is no trace of the ordinary foliage pinnules. At b and c 
are shown what appears to be the remains of a pair of lateral pinnae, each of 
which seems to have supported four fructifications. Associated with these 
pinnae are the remains of a small number of ordinary barren pinnules. Of 
the two lower pinnae, that marked d is very incomplete, and only shows some 
fragments of the ordinary barren pinnules; the corresponding opposite pinna 
is, however, more perfect, and shows three fructifications and a portion of a 
pedicel of a fourth. At the base of this pinnae are preserved some remains of 

* Quart. Jour. Geol. Soc, vol. iii. p. 424, pi. xxv. fig. le and 1/. 

f See Zeiller, ' ' Notes sur la Flore houillere des Asturies," Mem. Soc. Geol. du Nord. Lille, p. 6, 
1882. 

% See Goppert, " Foss. Farrnkrauter," Syst. fit. foss., p. 262, pi. xxxvi. fig. 4, Fxcipulites Neesii; 
Weiss, Foss. Flora d. jiing. SlJc. u. d. Rothl., p. 19; Schimper, Traite d. paleont. veget, vol. i. p. 141, 
pi. i. fig. 19, and Explanation to pi. xxxii. figs. 6 7 ; Geinitz, Vers. d. Steinh. in Sadisen, p. 2, pi. xxiii. 
fig. 13, Excipulites Neesii; pi. xxv. fig. 10, Depazites Rabenliorsti ; Feistmantel, "Der Handendflb'tzzug," 
&c, Archiv. d. Naturw. Landesdurchforschung von Bohmen, iv. Band, No. 6 (Geol. Abth.), p. 62, pi. i. 
fig. 1, Xylomides ellipticus; Weiss, " Steinkohlen-Calamarien," Abliandl. z. geol. specialJcarte v. Preussen 
u. d. Thiiringischen Staaten, Band v. Heft. ii. p. 66, pi. i. fig. 2; Grand' Eury, Flore carbon, du Depart, 
de la Loire et die centre de la France, p. 10, Excipidites punctatus and Hysterites cordaitis, pi. i. 
fig. 7, &c. 

§ Die Versteinerungen die Rothliegenden in Sachsen, p. 1 2, pi. iv. figs. 2, 3. 

|| See Weiss, Foss. Flora d. jung. Stic. u. d. Rothl., p. 27 ; also for the fruit of Odontopteris, see 
Gand' Eury, Flore carbon, du Depart, de la Loire, p. iii. pi. xiii. fig. 4. 



152 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

f 
the ordinary barren pinnules. It would appear, therefore, that each of the 
lateral pinnae supported four fruits, and on the terminal portion; though the 
remains of only eleven fructifications are seen, there were probably originally 
twelve. There may be combined in this part two lateral pinnae and the apex 
of the frond, each bearing four fruits, but this cannot be clearly traced. 
At/ is shown a small fragment of a pinna, drawn in the natural position it 
holds to the larger specimen. This shows the remains of two fructifications 
and portions of three barren pinnules, one of which is very perfect. The 
fortunate occurrence of barren pinnules associated with this fructification, 
conclusively identifies this interesting specimen with the genus Neuropteris, 
and further the barren pinnules/* and e* do not differ in any way from many 
shown on the figure of N. heterophylla, given by Brongniart in the Hist. d. 
Veget. foss., plate lxxi. In the same beds from which this specimen was 
collected N. heterophylla is plentiful. 

As to the affinities of this species, either with past or present existing 
genera of ferns, unfortunately this specimen does not afford sufficient data 
from which to form any opinion. 

In the description of this specimen, I have therefore refrained from employ- 
ing the terms indusium or sporangium to the little expansions at the 
extremities of the pedicels, as I cannot determine their true structure, though 
they are apparently composed of two or four segments. 

Horizon. — Lower Coal Measures. 

Locality. — Blairpoint, Dysart, Fife. 

Alcicornopteris, n. gen., Kidston. 

Generic Description. — Eachis ramifying by a series of dichotomies. Barren 
pinnse composed of a foliaceous RhacophyUum-\Hk.Q expansion. Fruiting 
portion consisting of much divided circinately convoluted pinnae. Form and 
mode of attachment of sporangia to the fruiting pinnae unknown. 

Remarks. — This genus in the barren condition ' approaches closely to 
Rhacophyllum, and in its fruiting branches to Schimper's Triphyllopteris 
collombi and Dawson's Cyclopteris acadica. 

Alcicornopteris convoluta, n. sp., Kidston. 
Plate VIII. figs. 11-15. 

Rhacophyllum Lacluca, Kidst. (not Sternb.), Trans. Roy. Soc. Edin., vol. xxx. p. 540. 

Description. — Rachis flattened with a central angular ridge, and dividing 
by a series of dichotomies. The primary (?) dichotomy forming an obtuse 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 153 

angle ; those angles formed by subsequent dichotomies are a little more acute. 
The pinnae of the barren fronds possess a broad foliaceous expansion cut into 
spirally bent lobes, in which the nerves are indicated by dichotomously 
dividing ridges. Fertile pinnae dividing dichotomously and reduced to winged 
circinately convoluted rachis-like segments. The convolutions of the basal 
portion of the pinnae overlap each other; their ultimate divisions are narrower, 
less prominently winged, and do not apparently overlap each other, or only 
do so to a limited extent. 

Remarks. — Specimens of this fern have been in the Collection of the Geolo- 
gical Survey of Scotland for many years, that figured on Plate VIII. fig. 13, 
having been collected by the late Mr Richard Gibbs about twenty-live years 
ago. The portions of the species with which I first met were fragments of the 
scorpiod fruiting pinnae. These, I thought, might perhaps belong to Triphyl- 
lopteris Collombi, Schimper,* or to Cyclopteris {Aneimites) Aoadica, Dawson,f 
both of which species have very close affinities to each other, if not specifically 
identical. 

Associated with the British examples, though careful examination was 
made, no barren pinnules were ever discovered that could be identified with 
either Schimper's or Dawson's ferns. 

It was only towards the end of 1884 that my difficulties in the identification 
of this fern were removed by Mr John Rhodes, Fossil Collector to the Geolo- 
gical Survey of England, finding the specimens figured on Plate VIII. figs. 11, 12, 
which show the barren condition of this plant. I had previously seen a small 
fragment of the barren condition of AUicornopteris convoluta from Docken 
Beck, Eskdale, collected by Mr A. Macconochie, one of the Fossil Collectors 
to the Geological Survey of Scotland, but had erroneously identified it as 
Rhacopliyllum Lactuca,\ to which small fragments have a great resemblance, 
so much is this the case, that with fragmentary specimens it is almost impossible 
to distinguish them. The fruiting portions of A. convoluta have apparently a 
more strongly winged rachis than occurs in Cyclopteris Acadica, or in Triphyl- 
lopteris Collombi; but here also small fragments of the ultimate segments of 
the fruiting portions of AUicornopteris convoluta would be with difficulty 
distinguished from fragments of the fruiting portions of the two ferns already 
mentioned (see Plate VIII. fig. 15). 

* Triyhyllopteris Collombi, Schinaper-Zittel, Handbuch der paleontologie, ii. Band, 1 Lief, p. 114, 
fig. 84, 1879; Traite d. paleont. veget., vol. i. p. 479, pi. cvii. fig. 13; "Les veget. foss. du terrain de 
trans, d. Vosges" (in Le terrain de trans, d. Vosges, by J. Koechlin-Schluniberger and "W. Ph. 
Schimper, Strasburg, 1862), p. 339, pi. xxvii. figs. 8-11 (Sphenopteris). 

f Cyclopteris (Aneimites) Acadica, Dawson, "Geological Survey of Canada," Fossil Plants of the 
Lower Carboniferous and Millstone Gh'it Form, of Canada, p. 26, pL vii. figs. 53-63, 1873 ; Acadian 
Geol, 2nd ed., p. 481, fig. 75, 1868; Quart. Jour. Geol. Soc, vol. xxii. p. 153, pi. viii. fig. 32, 1865. 

+ Trans. Roy. Soc. Edin., vol. xxx. p. 540. 

VOL. XXXIII. PART I. U 



154 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF 

On the other hand, when more perfect specimens are secured, the differences 
between the fruiting portions of A. convoluta and C. Acadica and T. Collombi 
are very well marked, and in the barren condition, the British species has no 
similarity with either Schimper's or Dawson's plants. 

It may be questioned if this new plant should not be included in Rhacophyl- 
lum, with which its barren pinnae have so great a resemblance, but against 
adopting this course is the fact that Rhacophyllum is essentially a Coal Measure 
genus, whereas A. convoluta has hitherto only been found in the Calciferous 
Sandstones, and then usually in the basement beds. Whatever view may be 
taken of the genus Rhacophyllum, whether as forming an individual genus or as 
a provisional one, only containing the accessory pinnules of other ferns, I am 
not in a position to decide ; but in regard to A. convoluta there can remain no 
doubt as to its being an autonomous fern, and not a portion of another species. 

In Triphyllopteris Collombi the fruit is borne at the extremity of the 
circinately bent segments, and it probably occupied a similar position on 
A. convoluta, but none of the specimens that have come under my notice have 
shown any traces of sporangia. 

Description of Specimens. — Specimen from Horncliffe Dean, near the Mill, 
Eiver Tweed, South of Horncliffe Village, Northumberland, collected by Mr 
J. Ehodes (Plate VIII. fig. 11), in the Collection of the Geological Survey of 
England. This specimen shows a small portion of a barren frond. The rachis 
is very stout, and gives off apparently alternate pinnse, possessing a midrib with 
a sharp angular ridge. This example is not well preserved, and does not show 
any perfect pinn?e or pinnules, but these were apparently cut into lobes, having 
curious spirally twisted segments, which at their point of separation formed an 
almost circular sinus giving the frond a curled appearance. 

Specimen from Eiver Tweed, 100 yards below Norham Castle, Northumber- 
land, collected by Mr J. Ehodes (Plate VIII. fig. 12), in the Collection of the 
Geological Survey of England. This specimen, though also fragmentary, is a 
very good example of the mode of ramification of Alcicornopteris convoluta. It 
exhibits a portion of a rachis 4 cm. long, and 5 mm. broad at the lower broken- 
over extremity, and 1 cm. wide immediately below the point where it bifurcates. 
The two arms of the first bifurcation go off from the parent rachis at almost 
right angles, and then again bifurcate. Both the upper forks of this second 
dichotomy arc broken over, but the lower arm on the left forms a third series 
of dichotomies. On this is borne the barren pinnules. A portion of one of 
the corresponding forks of the right hand dichotomy of the third series is also 
present. Here again the pinnules are badly preserved, but show the same 
characteristics as fig. 11. The rachis appears to have been flat, and traversed 
by a prominent vascular system which appears as a triangular ridge. The 
hclicoid nature of the frond is well shown on the frondose portion of this 
specimen. An imperfect fragment of a pinnule lies between the primary forks 



SOME FERNS FROM THE CARBONIFEROUS FORMATION. 155 

of the rachis, but its position there is accidental. The surface of the rachis is 
finely striated. 

Specimen from Cove Shore, east of Cove Harbour, Berwickshire, collected by 
the late Mr R. Gibbs (Plate VIII. fig. 13), in the Collection of the Geological 
Survey of Scotland. This specimen, which is preserved in a hard micaceous 
sandstone containing many vegetable fragments, shows probably a primary 
dichotomy of the rachis. Before the pinnule segments are reached, there also 
appears here a threefold diohotomy of the axis, similar to that shown in fig. 12. 

Except the main axis, the other portions of the specimen are indifferently 
preserved. The rachis is very distinctly striated longitudinally, and seems to 
have been originally flat, with a well-pronounced central angular ridge, probably 
representing the vascular system of the rachis. The portion of the rachis 
shown in this figure is so flat that it must be described as winged. In fact, 
the frondose expansion of the barren pinnae seems to be only a further develop- 
ment of this wing. 

Specimen from Long Craigs Bay, near Dunbar, Haddingtonshire, collected 
by Mr James Bennie (Plate VIII. fig. 14), in the Collection of the Geological 
Survey of Scotland. This example of a fruiting portion of the frond of A. 
convoluta from Long Craigs Bay is preserved in a fine-grained red shale. The 
main rachis and those springing from it are broadly winged, the vascular 
bundle appearing as an angular ridge running in the centre of the rachis. 
The lateral pinnae, of which only the basal portions are preserved, are best 
seen to the right of the figure, and consist of a series of dichotomously divided 
helicoid segments. The segments of these pinnae overlap each other, and 
produce an almost inextricable confusion of convolutions. 

Specimen from River Tweed, about 100 yards below Norham Castle, Northum- 
berland (PI. VIII. fig. 15). This specimen probably exhibits the ultimate divisions 
of the fertile pinnae, and a comparison of this figure with the fruiting examples 
Triphyllopteris Collombi, Schimper, figured in the Handbuch der Paleontologie, 
p. 144, fig. 87, and with the figures of Cyclopteris Acadica given by Dawson, 
in the Fossil Plants of the Loiver Carb. of Canada, plate vii., will show the great 
similarity between certain portions of these three ferns. The rachis in this 
part of the pinnae can scarcely be said to be winged, though distinctly flattened. 

Horizon. — Calciferous Sandstone series. 

Localities : — 

Scotland — Berivicksliire. — Cove Shore, \ mile east of Cove Harbour, 1^ miles 
north-east of Cockburnspath. " In a hard bed of micaceous sandstone at 
the base of the Carbonificerous Rocks, or rather at the base of that 
portion of them which immediately overlies the red and yellow sandstones of 
Berwickshire"* (R. Gibbs, collector) Kimmerghame Quarry, near Duns ; (A. 
Macconochie). Haddingtonshire. — Long Craigs Bay, east of Belhaven Bay, 

* "Memoirs of the Geol. Survey of Great Britain," The Geology of Eastern Berwickshire, p. 58, 1864. 



156 MR ROBERT KIDSTON ON THE FRUCTIFICATION OF FERNS, ETC. 

1 mile west of Dunbar (J. Bennie). Dumfriesshire. — Docken Beck, 3 miles 
south of Langholm (A. Macconochie). 

England — Northumberland. — River Tweed, 100 yards below Norham 
Castle; River Tweed, south of Horncliffe Village; Horncliffe Dean, near mill 
south of Horncliffe Village ; River Coquet, \ mile north-north-east of 
Holystone ; Coomsdon Burn, ^ mile south-west from its junction with the 
River Rede ; Hawk Burn, near Catcleugh, Reclesdale ; Spithope Bum, 
Redesdale ; Crawley Dean (east of road), ^ mile south of Powburn, near 
Ingram. Cumberland. — Bull Cleugh, Kirk Beck, Bewcastle. 

I am indebted, to Dr A. Geikie, F.R.S., for permission to figure and describe 
the various specimens, mentioned in this communication, belonging to the 
Geological Surveys of England and Scotland. 



EXPLANATION OF PLATE VIIT. 

Figs, l-6a. Calymmatotlieca bifida, L. & H., sp. 
Fig. 1. From Biver Irthing, near Lampert. 

Fig. 2. From Lewis Burn, near Lewis Burn Colliery, N. Tynedale, Northumberland. 
Fig. 3. From Back Burn, opposite Cranecleuch New Houses, N. Tynedale. 
Fig. 4. From Bateiughope Burn, Eedesdale. 
Fig. 5. Synangium, lettered a on fig. 4 ; enlarged. 
Fig. 6«.From Lewis Burn, near Lewis Burn Colliery, Northumberland. 
Fig. 6b. Sorodadus antecedens, Kidston. 

Fig. 7. Neuro-pteris heteropliylla, Brongt. From Blairpoint, Dysart, Fife. 
Figs. 8-10. Zeilleria Avoldensis, Stur, sp. From Coseley, near Dudley. 
Figs. 9-10. Pinnules ; enlarged. 
Figs. 11-15. Alcicornopteris convoluta, Kidston. 

Fig. 11. From Horncliffe Dean, River Tweed, Northumberland. 
Fig. 12. From Norham Castle, Northumberland. 
Fig. 13. From Cove Shore, east of Cove Harbour, Berwickshire. 
Fig. 14. From Long Craigs Bay, near Dunbar, Haddingtonshire. 
Fig. 15. From River Tweed, near Norham Castle, Northumberland. 

EXPLANATION OF PLATE IX. 

Figs. 16-17. Calymmatotlieca bifida, L. & H., sp. 

Fig. 16. From Burdiehouse, near Edinburgh. Specimen in the "Hugh Miller Collection," 

Museum of Science and Art, Edinburgh (natural size). 
Fig. Vlabc. Three Pinnules, enlarged. 
Fig. 18. Calymmatotlieca afifinis, L. & H., sp. From Burdiehouse, Mid-Lothian. 
Fig. 19. Calymmatotlieca afflnis, L. & H., sp. From Harwood Burn, below Limefield House, 
near West Calder. In the Collection of the Geological Survey of Scotland (fig. 19a, 
enlarged ; 19b, natural size). 
Fig. 20. Calymmatotlieca affinis, L. & H., sp. From West Calder, Mid-Lothian. Collected by 

the late Mr C. W. Peach. 
Figs. 21, 22. Calymmatotlieca affinis, L. & H. Copied from Peach, Quart. Jour. Geol. Soc, vol. 
xxxiv. pi. viii. figs, la (= 21) and 3-3fl (= 22a, b). 



( 157) 



VI. — On the Colours of Thin Plates. By Lord Rayleigh. (Plate X.) 

(Received 13th July 1886. Revised Aug. 1886.) 

Introduction. 

The first impression upon the mind of the reader of the above title will 
probably be, that the subject has long since been exhausted. The explanation 
of these colours, as due to interference, was one of the first triumphs of the 
wave-theory of light ; and what Young left undone was completed by Poisson, 
Fresnel, Arago, and Stokes. And yet it would be hardly an exaggeration 
to say that the colours of thin plates have never been explained at all. The 
theory set forth so completely in our treatises tells us indeed how the com- 
position of the light reflected depends upon the thickness of the plate, but what 
will be its colour cannot, in most cases, be foretold without information of an 
entirely different kind, dealing with the chromatic relations of the spectral 
colours themselves. This part of the subject belongs to Physiological Optics, 
as depending upon the special properties of the eye. The first attempt to deal 
with it is due to Newton, who invented the chromatic diagram, but his represen- 
tation of the spectrum is arbitrary, and but a rough approximation to the 
truth. It is to Maxwell that we owe the first systematic examination of the 
chromatic relations of the spectrum, and his results give the means of predicting 
the colour of any mixed light of known composition. Almost from the time 
of first reading Maxwell's splendid memoir, I have had the wish to undertake 
the task of calculating from his data the entire series of colours of thin plates, 
and of exhibiting them on Newton's diagram. The results are here presented, 
and it is hoped may interest many who feel the fascination of the subject, and 
will be pleased to see a more complete theory of this celebrated series of 
colours. 

The diagram (Plate X.) explains many things already known from observa- 
tion, such as the poverty of the blue of the first order and of the green of the 
second order. For good blues we must look to the second and third orders, and 
for good greens to the third and fourth. The point in which the diagram dis- 
agrees most with descriptions by former observers, e.g., Herschel, relates to the 
precedence of the reds of the first and second orders. The first red has usually 
been considered inferior, but the reason appears to lie in its feeble luminosity, 
and consequent liability to suffer from contamination of white light. This and 
other questions are further discussed in the sequel. 

VOL. XXXIII. PART I. X 



158 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

The complementary colours, best obtained with the aid of polarised light, 
are also calculated and exhibited on a diagram. 

§ 1. The calculation, according to Young and Poisson, of the amount of 
light of given wave-length (X) reflected from a thin plate is given in all treatises 
on physical optics. If D be the thickness, /3 the obliquity of the ray within 
the plate, 1 : e, the ratio in which the amplitude is altered in one reflection, 
then for the intensity of light in the reflected system we have— 

4^sin2(7rV/X) -. 

(l-e 2 ) 2 + 4e 2 sin 2 (7rV/A) { } 

in which the intensity of the original light is taken to be unity, and V is 
written for 2 D cos /3. The colours exhibited in white light are to be found 
by combining the chromatic effects of all the rays of the spectrum. 

When, as in Newton's rings, the thickness of the plate varies from point to 
point, there is a series of colours determined by supposing D to vary in the 
above expression. This series is not absolutely independent of the material of 
which the plate is composed, even if we disregard the differences of brightness 
corresponding to the occurrence of e 2 in the numerator of our expression. On 
account of retarded propagation, the value of X for a given ray is less in glass, 
for instance, than in air ; and in consequence of dispersion there is no accurate 
proportionality, so that we cannot say absolutely that a definite thickness in 
glass corresponds to a definite, though different, thickness in air. Moreover, 
since e varies from one body to another, the denominator of (1) changes its 
value somewhat. 

It is evidently impracticable to carry out calculations strictly applicable to 
all cases. If we take for X the wave-length in air, we obtain results appropriate 
to the ordinary case of Newton's rings ; and in extending them to plates of 
other material, we in effect neglect the relatively small influence of dispersion. 

Again, we may without much error neglect the variation of the denomin- 
ator with wave-length, which amounts to supposing e 2 small, or that the two 
media do not differ much in refrangibility. In the case of glass and air the 
value of e 2 is about ^5. When sin 2 (7rV/X) is small, it is of little consequence 
what the value of the denominator may be, and we may therefore identify it 
with (1 + e 2 ) 2 , taking instead of (1), 

4e 2 . „ 7rV /on 

sin 2 (2) 



(1+e 2 ) 2 " X 

It is on this formula, strictly applicable only to a plate of air bounded by 
matter of small refrangibility, that the calculations and diagrams of this 
investigation are based. 

§ 2. The colours of Newton's scale are met with also in the light transmitted 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 159 

by a somewhat thin plate of doubly-refracting material, such as mica, the plane 
of analysis being perpendicular to that of primitive polarisation. To this case 
also our calculations are applicable, if we neglect the dispersion, and (as is 
usual) the light transmitted after two or more reflections at the surfaces of 
the plate. 

If the analyser be turned through 90°, a new series of colours is exhibited 
complementary to the first series. The purity of the colours, as regards 
freedom from admixture with white, is greatest when the principal section of 
the crystal is inclined at 45° to the plane of polarisation, and it is in this case 
also that the colours of the first series attain their maximum brightness. If 
we represent the first series by sin 2 (7r V/X), the second series in the case referred 
to will be represented by cos 2 (7rV/X). It should be noticed that the colours of 
Newton's rings seen by transmitted light are complementary to those seen 
by reflection; but the scale of colours is far more dilute than that obtainable 
as above with the aid of double refraction. 

The colours of the first series are met with also in other optical experi- 
ments, e.g., at the centre of the illuminated patch, when light issuing from a 
point passes through a small round aperture in an otherwise opaque 
screen.* 

§ 3. In order to be able to calculate the colour of any given mixture of light, 
it is necessary to know the exact chromatic relations of the spectral rays them- 
selves. This is precisely the question investigated by Maxwell, t Selecting 
three rays as standards of reference, he expresses the colours of other rays in 
terms of them. The actual observations in all cases consisted in matches of two 
whites, one the original white which had not undergone prismatic analysis, the 
other a white compounded of three rays, — first of the three standard rays 
themselves, then of two standard rays in combination with a fourth ray which 
it was desired to express in terms of the standards. The auxiliary white was 
then eliminated. 

The three points selected were at 24, 44, and 68 of the scale to which 
the spectrum was referred. "I chose these points, because they were well 
separated from each other on the scale, and because the colour of the spectrum 
at these points does not appear to the eye to vary very rapidly, either in hue or 
in brightness, in passing from one point to another. Hence, a small error of 
position will not make so serious an alteration of colour at these points, as if 
we had taken them at places of rapid variation; and we may regard the 
amount of the illumination produced by the light entering through the slits in 
these positions as sensibly proportional to the breadths of the slits. 



* Airy's Tract on Optics, § 79. 

f "On the Theory of Compound Colours," Phil. Trans., 1860. 



160 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

" (24) corresponds to a bright scarlet about one-third of the distance from 
C to D ; (44) is a green very near the line E ; and (68) is a blue, about one- 
third of the distance from F to G." 

A specimen observation is given : — 

" Oct. 18, J. 18-5(24) + 27(44) + 37(68) = W . 

This equation means that on the 18th of October the observer J (myself), 
made an observation in which the breadth of the slit X was 18-5, as measured 
by the wedge, while its centre was at the division (24) of the scale ; that the 
breadths of Y and Z were 27 and 37, and their positions (44) and (68) ; and 
that the illumination produced by these slits was exactly equal, in my estima- 
tion as an observer, to the constant white W. 

" The position of the slit X was then shifted from (24) to (28), and when 
the proper adjustments were made, I found a second colour-equation of this 
form — 

Oct. 18, J. 16(28) + 21(44) + 37(68) = W . 

Subtracting one equation from the other, and remembering that the figures 
in brackets are merely symbols of position, not of magnitude, we find 

16(28) = 18-5(24) + 6(44), 

showing that (28) can be made up of (24) and (44), in the proportion of 18-5 
to 6. 

" In this way, by combining each colour with two standard colours, we may 
produce a white equal to the constant white. The red and yellow colours from 
(20) to (32) must be combined with green and blue, the greens from (36) to 
(52) with red and blue, and the blue from (56) to (80) with red and green." 

The values employed in the present paper are those of Maxwell's second 
observer K (whose vision in the region of the line F was more normal than his 
own)*, and are given in his table No. VI. For our purpose they require some 
extension, especially at the violet end. Thus the equivalents of (16), (84), (88), 
(92), (96), (100), are obtained by a graphical extrapolation from the curves given 
by Maxwell. The adjoining table is deduced from his with some reduction, in 
order to exhibit the value, in terms of the three standards, of the illumination 
due to the unit width of slit in each case. It will be seen that the extrapola- 
tion at the upper end of the spectrum is necessary in order to make up 
anything like the full total of (68). 

* It is understood that K represents Mrs Maxwell. In these matters a woman's observations are 
generally to he preferred to a man's, as less liable to irregularities of the kind described in Nature, Nov. 
17, 1881. 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 



161 



Table I. 



Scale. 


Wave-length. 


Colour. 


(24) 


(44) 


(68) 


16 


2580 


red 


+440 






20 


2450 


red 


•420 


+ •009 


+ ■063 


24 


2328 


scarlet 


1000 






28 


2240 


orange 


1-155 


•360 


-•006 


32 


2154 


yellow 


•846 


•877 


•005 


36 


2078 


yellow-green 


484 


1-246 


•032 


40 


2013 


green 


+ •127 


1-206 


-•008 


44 


1951 


green 




1-000 




48 


1879 


bluish-green 


-•063 


•759 


+ •085 


52 


1846 


blue-green 


•055 


•506 


•282 


56 


1797 


greenish-blue 


•050 


•340 


•495 


60 


1755 


blue 


•047 


■190 


•753 


64 


1721 


blue 


-033 


•033 


•905 


68 


1688 


blue 






1-000 


72 


1660 


indigo 


+ 019 


•006 


•944 


76 


1630 


indigo 


•025 


+ •016 


•693 


80 


1604 


indigo 


•005 


-028 


•479 


84 


1580 








•333 


88 


1560 






* • • 


•208 


92 


1540 




. . . 




•146 


96 


1520 


. . . 






•083 


100 


1500 


... 






•042 








+ 3973 


+ 6-520 


+ 6460 



The colour produced by combining all the light which passed the prisms 
from (16) to (100) is the white of the apparatus. Its equivalent in terms of 
the standards is given by 

W' = 3-973(24) + 6-520(44) + 6-460(68). 

It differs a little from the standard white of the original matches, i.e., 

W = 18-6(24) + 31-4(44) + 30'5(68) , 

not only in consequence of omission of some extreme red and violet, but 
probably also on account of absorption by the prisms. 

The colours of the spectrum were exhibited by Maxwell in Newton's 
manner, and are reproduced on our diagram (Plate X.), in which each colour 
is represented by the centre of gravity of three weights at the corners of an 
equilateral triangle, the magnitudes of the weights being taken proportional to 
the quantities of (24), (44), and (68) required to compound the colour, so that 
the corners themselves represent the standard colours. 

The wave-lengths are given in Frauenhofer's measure (in terms of the Paris 
inch).* The scale is such that for D, X = 2175, and for F, X = 1794. 



* 1 Paris inch = 2-7070 cm. 



102 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 



The fact that the spectrum colours lie, roughly speaking, upon two sides of 
the triangle (see Plate X.), indicates that all pure oranges and yellows can be 
made up by a mixture of pure red and pure green, and in like manner that 
all varieties of pure blue and blue-green can be compounded of pure violet and 
pure green. If, as there is reason to believe, the curve representing the 
spectrum is slightly rounded off at the green corner, this means that the 
same spectrum green is not available for both pure yellows and pure blues. 
The green lying most near the corner gives with red yellows, and with violet 
blues, which are somewhat less saturated than the corresponding colours of the 
spectrum. 

Table II. 





Sin*^ 








A 




- 


V = 1846 


V=3600 


V-6800 


16 


•607 


•896 


•828 


20 


•490 


•991 


•420 


24 


•367 


•980 


•060 


28 


•275 


•892 


•013 


32 


•188 


•737 


•225 


36 


•118 


•553 


•572 


40 


•066 


•379 


•863 


44 


•028 


•219 


1-000 


48 


•003 


•068 


•865 


52 


•000 


•024 


•702 


56 


•007 


•000 


•391 


60 


•026 


•026 


•148 


64 


•052 


•081 


•023 


68 


•084 


•164 


•008 


72 


•119 


•256 


•089 


76 


•164 


•373 


•264 


80 


•209 


•483 


•467 


84 


•255 


•589 


•667 


88 


•297 


•678 


•817 


92 


•342 


•762 


•932 


96 


•389 


•840 


•994 


100 


•440 


•904 


•989 



§ 4. The colours of thin plates are to be calculated in accordance with (2) 
from Table I., as white was calculated, but with introduction throughout of the 
factor sin 2 (7rV/X). For each thickness of plate V is constant, but an integration 
over the spectrum is required. Table II, gives a specimen of the- values of the 
factors, and may be considered to represent the brightness, at various points, 
of thespectrum that would be formed by analysing the light reflected. The 
three retardations given correspond to the reds of the first and second order, 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 



163 



and to the green of the fourth order. In actual calculation these numbers 
would not occur (nor indeed those of Table I.), but would be represented by 
their logarithms. 

From the necessity of determining a large number of points, the calculations 
ran to great length. They have not been performed throughout in duplicate, 
but have been so far re-examined as to exclude any error which could appreciably 
affect the diagram. In many cases neighbouring points verify one another to 
a sufficient degree of accuracy. 

Table III. — First Series. 



V. 


(24). 


(44). 


(68). 


V. 


(24). 


(44). 


(68). 





•77 


1-65 


2-28 


5200 


2-69 


472 


1-42 


1006-5 


3-82 


6-46 


5-87 


5300 


3-06 


430 


1-95 


1300 


3-75 


5-07 


2-79 


5400 


3-33 


3-78 


2-68 


1500 


3-01 


3-20 


•82 


5600 


351 


2-75 


415 


1604 


2-51 


2-23 


•27 


5800 


3-20 


2'01 


5-03 


1688 


204 


1-49 


■18 


6000 


2-53 


1-77 


4-93 


1755 


1-67 


1-01 


•27 


6200 


1-75 


2-11 


3-97 


1846 


1-20 


•53 


•69 


6400 


1-09 


2-82 


2-74 


1951 


•75 


•26 


1-63 


6600 


0-76 


3-56 


1-85 


2013 


•49 


•26 


2-25 


6700 


0-74 


3-87 


1-71 


2154 


•13 


•67 


3-81 


6800 


0-83 


4-12 


1-75 


2328 


•09 


1-82 


5-44 


6900 


1-00 


4-26 


1-99 


2630 


•99 


4-44 


5-87 


7000 


1-26 


4-32 


2-41 


2927 


2-59 


5-95 


3-37 


7100 


1-55 


4-27 


2-91 


3100 


3-29 


5-77 


1-71 


7200 


1-86 


4-13 


3-41 


3300 


3-78 


4-68 


•59 


7400 


2-45 


369 


417 


3400 


3-81 


4-04 


•58 


7600 


2-83 


3-16 


4-48 


3500 


3-74 


3-17 


•93 


7800 


2-93 


2-76 


4-02 


3600 


3-50 


2-40 


1-59 


8000 


2-72 


2-56 


3-24 


3800 


2-68 


1-26 


3-42 


8200 


2-35 


2'62 


2-45 


4000 


1-67 


•93 


5-08 


8400 


1-89 


2-85 


2-28 


4200 


•79 


1-48 


5-71 


8600 


1-52 


317 


2-52 


4400 


•29 


2-68 


5-02 


8800 


1-32 


3-47 


2-98 


4600 


•35 


3-96 


3-43 


9000 


1-34 


3-65 


3-69 


4800 


•91 


4-91 


1-86 


9200 


1-53 


3-73 


4-04 


4900 


1-33 


5-13 


1-31 


9400 


1-83 


3-67 


3-84 


5000 


1-79 


5-17 


1-03 











The final results, expressed as before in terms of the standards (24), (44), (68), 
are exhibited in Table III. In the first column are to be found the values of 
V (expressed in the same measure as A.). Thus, when V = 1688, the illumina- 
tion vanishes at the point (68) on Maxwell's scale, for which X=1688. If the 
compound light reflected from a plate of this thickness were analysed by the 
prism, the centre of a dark band would be found at (68). Although the 
extinction is absolute at only one point, still the neighbouring region, which 
naturally contributes most of the colour-component (68), is very obscure, and 



164 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

thus the total of this component reaches only 178, while the two other com- 
ponents are present in fair quantity. The resulting colour is a good orange. 

As V increases, the dark band moves down the spectrum. When V = 1951, 
the centre of the band is at (44) ; thus nearly all the green is eliminated, 
and the colour is a rich purple. Again, when V = 2328, the centre of the band 
is at (24), the resulting colour is a rich blue. This band then moves out of the 
visible spectrum ; but a new one presently makes its appearance, and begins 
to invade the spectrum from the violet end. When V = 2 x 1688 or 3376, the 
ray (68) is again extinguished, and the colour is the yellow of the second order. 
For higher values of V, there may be two or more dark bands simultaneously, 
as appears in Table II., when V = 6800. 

§ 5. Any sequence of colours may conveniently be represented on Newton's 
diagram, in the manner adopted by Maxwell for the particular sequence found 
in the spectrum. Such a curve would represent, for example, the colours of an 
absorbing medium, as the thickness traversed varies from nothing to infinity. 
In all suck cases the cui've starts from the point white, and ends at the point 
representative of that ray of the spectrum to which the medium is most trans- 
parent. For many coloured media the curve would not depart widely from a 
straight line ruled ont wards from white to a point on one of the sides of the 
triangle. But when the medium is dichromatic, as for example a solution of 
chloride of chromium, the curve might start in one direction and ultimately 
come round to another. Thus in the case referred to the course of the curve 
from white would be towards the middle of the blue side of the triangle, then 
after a good progress in that direction it would bend round through yellow, and 
ultimately strike the triangle at a point near the red corner representative of 
the extreme visible rays at the lower end of the spectrum. The principal object 
of the present investigation was to exhibit in a similar manner upon Newton's 
diagram the curve of the colours of thin plates. To find the point correspond- 
ing to the retardation 1688, we imagine weights proportional to the numbers 
2 - 04, 1*49, "18 to be situated at the three angular points of the triangle, and 
construct the centre of gravity of such weights. This point represents the 
colour due to retardation 1688. 

§ 6. The diagram (Plate X.) embodies the results of Table III., so far as the 
quality of the effects is concerned. When the thickness, or retardation (V), is 
infinitely small, the amount of light reflected of course vanishes, but the colour 
approaches a limit, found by combining the constituents in quantities propor- 
tional to \~' 2 , the limit of sin 2 (7rV/\). This limiting blue of the first order 
would be the blue of the sky, according to the theory which attributes the light 
to reflection from thin plates of water in the form of bubbles. The blue of the 
sky is, however, really a much richer colour than this, and corresponds more 
nearly to that calculated on the supposition that the disturbance is due 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 165 

to spheres, or masses of other shape, small in all their dimensions relatively 
to the wave-lengths of light. According to this view, the colour is that 
found by taking the components of white light proportionally to X -4 , instead 
of X~ 2 .* 

The curve, starting thus from a definite point, takes a nearly straight course 
in the direction of white (W), which it passes a little upon the green side. The 
white of the first order on Newton's scale is thus somewhat greenish, as must 
obviously be the case when we consider that it arises when the maximum 
reflection is in the green or yellow portion of the spectrum, so that the red and 
blue must be relatively deficient ; but the deviation from white is very small, 
and is not usually recognised. After leaving white the curve passes through 
the yellow, and approaches pretty close to the side of the triangle at a point 
representing the D-line in the orange.t The retardation is here 1688. The 
colour then reddens, but makes no approach to the spectrum reds lying near 
the corner of the triangle. Passing rapidly through the purple "transition- 
tint," it becomes bluer, until it attains the magnificent blue or violet of the 
second order, in the neighbourhood of V = 2328. At this.point there is a good 
approach to the corresponding spectrum colour, although the latter lies here a 
little outside the triangle. Leaving blue the colour rapidly deteriorates, 
becoming greener, but nowhere attaining a good green. The best yellow of the 
second order at 3400 is nearly as pure as the best of the first order, but inclines 
less to orange. The reds of the second order are even less pure than those of 
the first, but the inferiority diminishes as we approach the second transition- 
tint in the purple. The blue of the third order at 4200 is much inferior to the 
corresponding colour of the second order, but gradually acquires a superiority 
as it becomes greener near 4400. The blue-greens which follow, and the full 
greens from 4800 to 5000, are splendid colours, beyond comparison superior to 
the corresponding colours of the second order, but yet falling far short of the 
spectrum colours near (44). On the other hand, in the third order the yellows 
are not so pure as in the first and second orders, and there is even less 
approach to red, although a better show is made in the purple at 6000. In the 
transition from this purple to green, the blue falls short even of the blue of the 
first order, but the green at 6800 is very fine, sensibly equal to one of the 
greens of the third order. It will be remarked that in the fourth order greens 
there is little variety, the direction both on the outward and on the backward 
course being nearly in a line through white. On the return to white, which is 

* See several papers by the Author, published in the Philosophical Magazine, " On the Light from 
the Sky, its Polarisation and Colour," Feb. 1871, April 1871 ; "On the Scattering of Light by small 
Particles," June 1871 ; " On the Electro-Magnetic Theory of Light," August 1881, &c. 

t The points 20, 24, 28, .... on the diagram, represent the spectrum colours as determined by 
Maxwell. 

VOL. XXXIII. PART I. Y 



166 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

very closely approached, a contrary curvature sets in, so that the earlier reds 
are more blue than the later. The curve then bends round on the yellow side 
of white, until it attains a rather feeble blue-green at 9000. 

§ 7. It will be interesting to compare the diagram with descriptions by 
previous writers of Newton's scale of colours. In his article on Light in the 
Encyclopaedia Met ropolitana (1830), Sir John Herschel says: — "The colours, 
whatever glasses be used, provided the incident light be white, always succeed 
each other in the same order ; that is, beginning with the central black 
spot as follows : — 

" First ring, or first order of colours, — Black, very faint blue, brilliant white, 
yelloiv, orange, red. 

" Second ring, or second order, — Dark purple or rather violet, violet, blue, 
green (very imperfect, a yellow-green), vivid yellow, crimson-red. 

"Third ring, or third order, — Purple, blue, rich grass-green, fine yellow, pink, 
crimson. - 

"Fourth ring, or fourth order, — Green (dull and bluish) , pale yellowish-pink, red. 
" Fifth ring, or fifth order, — Pale bluish-green, white, pink. 
" Sixth ring, or sixth order, — Pale blue-green, pale pink. 
"Seventh ring, or seventh order, — Very pale bluish-green, very pale pink. 
"After these the colours become so pale that they can scarcely be dis- 
tinguished from white. 

" On these we may remark, that the green of the third order is the only one 
which is a pure and full colour, that of the second being hardly perceptible, 
and of the fourth comparatively dull and verging to an apple-green; the yellow 
of the second and third orders are both rich colours, but that of the second is 
especially rich and splendid ; that of the first being a fiery tint passing into 
orange. The blue of the first order is so faint as to be scarce sensible, that of 
the second is rich and full, but that of the third much inferior ; the red of the 
first order hardly deserves the name— it is a dull brick-colour ; that of the 
second is rich and full, as is also that of the third ; but they all verge to 
crimson, nor does any pure scarlet or prismatic red occur in the whole series." 

Herschel's observations were made in the usual way with glass lenses, — a 
course convenient in respect of measurement of thicknesses, but incapable of 
doing justice to the colours, in consequence of the contamination with white 
light reflected at the upper surface of the upper plate and at the lower surface 
of the lower plate. The latter reflection should at any rate be got rid of by 
using a glass, either opaque, or blackened at the hind surface. 

§ 8. For his description Newton used the soap-bubble, " because the Colours 
of these Bubbles were more extended and lively than those of the Air thin'd 
between two Glasses, and so more easy to be distinguished." He takes the 
colours in the reverse order, beginning with large retardations. I give his 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 167 

description as nearly as may be in his own words, but adapted to the more 
convenient notation followed by Herschel : — 

" The red of the fourth order was also dilute and dirty, but not so much as 
the former three ; after that succeeded little or no yellow, but a copious green 
(fourth order), which at first inclined a little to yellow, and then became a pretty 
brisque and good willow-green, and afterwards changed to a bluish colour ; 
but there succeeded neither blue nor violet. 

"The red of the third order inclined very much to purple, and afterwards 
became more bright and brisque, but yet not very pure. This was succeeded 
with a very bright and intense yellow, which was but little in quantity and soon 
changed to green ; but that green was copious and something more pure, deep 
and lively than the former green. After that followed an excellent blue of a 
bright sky colour (third order), and then a purple, which was less in quantity 
than the blue, and much inclined to red. 

" The red of the second order was at first a very fair and lively scarlet, and 
soon after of a brighter colour, being very pure and brisque, and the best of all 
the reds. Then after a lively orange followed an intense bright and copious 
yellow, which was also the best of all the yellows ; and this changed first to a 
greenish-yellow and then to a greenish-blue ; but the green between the yellow 
and the blue was very little and dilute, seeming rather a greenish- white than a 
green. The blue which succeeded became very good, and of a very fair bright 
sky-colour, but yet something inferior to the former blue ; and the violet was 
intense and deep, with little or no redness in it, and less in quantity than the 
blue. 

" In the last red appeared a tincture of scarlet next to violet, which soon 
changed to a brighter colour, inclining to an orange ; and the yellow which 
followed was at first pretty good and lively, but afterwards it grew more dilute, 
until by degrees it ended in perfect whiteness."* 

§ 9. Some small discrepancies in the descriptions of Newton and Herschel 
probably depend upon ambiguities in the use of colour names. In the rings of 
high order what Newton calls blue, Herschel describes as bluish-green. Both 
observers remark upon the poverty of the green of the second order, but the 
diagram shows that it is superior to that of the fifth order. Neither Newton 
nor Herschel seem to have done full justice to the green of the fourth order, 
which at its best rivals closely the corresponding colour of the third order. 
My own observations are in accordance with the teaching of the diagram, which 
shows, moreover, that as we depart from retardation 6800 the colour of the 
fourth order rapidly deteriorates by admixture with white, while the colours of 
the third order in the neighbourhood of 4800 retain their purity as they change 
in hue. 

* Newton's Opticks, 1704, book ii. p. 21. 



168 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

One discrepancy between the diagram and the above descriptions will at 
once strike the reader. According to the diagram, the red and purple of the 
first order are superior to those which follow, whereas Herschel says that the 
red of the first order hardly deserves the name. Judged by the standard of 
the spectrum red at (24), this criticism would apply to them all; but the 
question is as to the relative merits of the various reds. The explanation 
depends upon considerations of brightness, of which the curve takes no account. 
If we refer to Table III., we see that at 1846 the red component is 1*20, but 
that at the corresponding point for the red of the second order (between 3600 
and 3800) it rises to about 30. The deficiency of brightness in the first order 
goes a long way by itself to explain the apparent inferiority, for dark red gives 
rather the impression of brown ; but if there is the slightest admixture of white 
light, the comparison is still more unfair. It would be useless, for example, to 
take the colours from an air-plate between lenses. The feebly luminous red of the 
first order is then drowned in a relatively large proportion of white light, which 
tells much less upon the brighter, though less pure, red of the second order. This 
complication does not arise when soap-films are employed, and the red of the 
first order is evidently much improved ; but the rapidity of transition at this 
part of the scale renders observation difficult. The best comparison that I have 
been able to make is with the aid of a beautiful mica combination kindly lent 
me by Eev. P. Sleeman. When this is examined in a dark room between 
crossed nicols, and lighted brilliantly from a part of the sky near the sun, the 
red of the first order is seen in great perfection, and I had no difficulty in 
believing it to be superior to that of the second order. It is not very easy to 
bring the rivals into juxtaposition under equal brightnesses ; but there is, I 
think, no reason to doubt that the first order would come off victorious. The 
composition of the lights will be understood by reference to Table II. 

§ 10. The only colours which can be said to make any approach to spectrum 
purity are the yellows of the first two orders, and the blue and green-blue of 
the second and third orders respectively. There is a corresponding difficulty 
in obtaining good greens by absorption. To do so it is necessary that the 
transmitted spectrum should terminate at two pretty well-marked points ; in 
the case of red the difficulty is much less, all that is requisite being that the 
transmission should increase rapidly as the refrangibility of the light diminishes. 

Besides the absolute brightness, there are two other circumstances which 
may influence the estimation of the colours of thin plates as normally presented. 
It is probable that in some cases the colours are much affected by contrast with 
their neighbours. To this cause we may attribute the difficulty in observing 
the transition between the reds and blue-greens of the fourth and higher 
orders. As the nearly neutral transition-tint is approached from either side, 
the effect upon the eye is improved by contrast, so as largely to compensate 



LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 169 

for the increasing poverty of the real colour. Much, again, depends upon the 
rapidity with which differences occur with varying retardation. When Newton 
speaks of the yellow of the second order as copious, he refers (I imagine) 
rather to the width of the band than to the brightness of the light. The 
diagram gives important information on this subject also. Compare, for 
example, in the first order, the change from 1500 to 1755, with that from 1755 
to 1846 or 1951. The rapidity of the change in the latter interval is the 
foundation of the usefulness of the " transition-tint " in polarimetric work. If 
we wish to compare the rates of progress in different orders, we must dis- 
tinguish according as we contemplate sensitiveness to small absolute, or to 
small relative, variations of retardation. 

§ 11. The points of intersection of the curve are of interest, as corresponding 
to colours obtainable with two different thicknesses. The first that presents 
itself is the yellow, common to the first and second order. The table shows 
that the latter is the brighter. In the second and third orders the similar 
colours differ but little in brightness. One occurs in the blue and another in 
the greenish-yellow. Nor is there much difference of brightness between 
the otherwise nearly identical greens of the third and fourth orders. It follows 
that if observers are able to distinguish in all cases which order of colours they 
are dealing with, it must be by reference to a sequence, rather than by estima- 
tion of a single colour. 

§ 12. With respect to the absolute retardations or thicknesses at which the 
various colours are formed, careful observations have been made by Reinold 
and Rucker.* For comparison with their results I will take the green of the 
fourth order at 6800. In air at perpendicular incidence, this answers to a 
thickness of 340 x 10" 5 Paris inches, or 919 x 10~ 5 cm. The numbers in their 
Table (p. 456), Column V., are 

Green, ...... 8 - 41 

8-93 

Yellow-green, ...... 9*64 

so that the agreement is pretty good. I would remark in passing that the 
diagram does not recognise a yellow-green of this order ; but the appearance 
of such may perhaps be explained by contrast. 

§ 13. The series of colours complementary to those of Table III. are found 
by subtraction of the numbers there given from those representative of white, 
viz., 397, 6'52, 6*46, respectively. The resulting numbers are exhibited in Table 
IV., in which the first entry for zero retardation corresponds to the full white, t 

* "On the Electrical Resistance of Thin Liquid Films, with a Revision of Newton's Table of 
Colours," Phil. Trans., 1881. 

f In comparing with Table III., it should be remembered that the numbers there given under the 
head of V = are relative only, the true values being infinitely small. 

VOL. XXXIII. PART I. Z 



170 LORD RAYLEIGH ON THE COLOURS OF THIN PLATES. 

Table IV. — Second (Complementary) Series. 



V. 


(24). 


(44). 


(68). 


V. 


(24). 


(44). 


(68). 





3-97 


6-52 


6-46 


5200 


1-28 


1-80 


5-04 


1006-5 


•15 


•06 


•59 


5300 


•91 


2-22 


4-51 


1300 


•22 


1-45 


3-67 


5400 


•64 


2-74 


378 


1500 


•96 


3-32 


5-64 


5600 


•46 


3-77 


2-31 


1604 


1-46 


4-29 


619 


5800 


•77 


4-51 


1-43 


1688 


1-93 


5-03 


6-28 


6000 


1-44 


4-75 


1-53 


1755 


2-30 


5-51 


6-29 


6200 


2'23 


4-41 


2-49 


1846 


2-77 


5-99 


5-77 


6400 


2-89 


3-70 


3-72 


1951 


3-22 


6-26 


4-83 


6600 


3-22 


2-96 


4-61 


2013 


3-48 


6-26 


4-21 


6700 


3-23 


2-65 


475 


2154 


3-84 


5-85 


2-65 


6800 


3-14 


2-40 


4-71 


2328 


3-88 


4-70 


1-02 


6900 


2-97 


2-26 


4-47 


2630 


2-98 


2-08 


•59 


7000 


2-72 


2-20 


4'05 


2927 


1-38 


•57 


3-09 


7100 


2-42 


2-25 


3-55 


3100 


•68 


•75 


4-75 


7200 


211 


2-39 


3-05 


3300 - 


•19 


1-84 


5-87 


7400 


1-52 


2-83 


2-29 


3400 


•16 


2-48 


5-88 


7600 


1-14 


3-36 


1-98 


3500 


•23 


3-35 


5-53 


7800 


1-04 


3-76 


2-44 


3600 


•47 


412 


4-87 


8000 


1-25 


3-96 


3-22 


3800 


1-29 


5-26 


3-04 


8200 


1-63 


3-90 


4-01 


4000 


2-30 


5-59 


1-38 


8400 


2-08 


3'67 


418 


4200 


3-19 


5-04 


•75 


8600 


2-45 


3-35 


3-94 


4400 


3-68 


3'84 


1-44 


8800 


2-65 


3-05 


3-48 


4600 


362 


2-56 


3-03 


9000 


2-63 


2-87 


2-77 


4800 


3-06 


1-61 


4-60 


9200 


2-44 


2-79 


2-42 


4900 


2-64 


1-39 


515 


9400 


215 


2-85 


2-62 


5000 


2-18 


1-35 


5-43 











The curve representative of this series of colours on Newton's diagram is given 
by the dotted line in the Plate, so far as the tabulated numbers permit. It 
starts from the point White, and passes rapidly through a whitish-yellow to a 
very dark red and purple at V = 1006 5. This part of the curve can not be 
drawn from the tabulated data, — a defect of no great consequence, for the 
quantity of light being so insignificant, its quality is of little interest. From 
V = 1300 onwards the curve is pretty well determined. 

It will be seen that the two series of colours are of pretty much the same 
general character. The green at 5800 in the second series compares favour- 
ably with the greens of the third and fourth orders in the first series. 



R S E Vol XXXIII PI X 




Ardia>allJ.I'«k£irSrarws K&n' 



( 171 ) 



VII. — On the Electrical Properties of Hydrogenised Palladium, By Cargill G. 
Knott,D.Sc. (Edin.),F.RS.E., Professor of Physics, Imperial University, 
Tokay o, Japan. (Plate XI.) 

(Despatched to Royal Society of Edinburgh, May 25, 1886. Read 19th July 1886.) 

In the following paper I desire to place on record the results of certain 
experiments which have lately engaged my attention. The facts established 
are, so far as I am aware, novel and in themselves interesting. 

Many of the physical properties of hydrogenised palladium or hydrogenium 
have been carefully studied by Graham, Dewar, and others ; but no one seems 
to have called attention to its thermoelectric peculiarities, or to have made a 
special study of its electrical resistance. These two inquiries form the subject 
of this paper. Throughout I shall use, for brevity's sake, the name Hydrogenium, 
which was applied by Graham to the fully-saturated form. Here, however, it 
is applied generally to any alloy of the two substances, without any regard to a 
possible chemical compound of definite molecular constitution. The paper 
naturally divides itself into two sections — the first part relating to the electrical 
resistance, the second part to the thermoelectric properties. 

Electrical Eesistance of Hydrogenium. 

The steady increase of the resistance of hydrogenium with the charge of 
hydrogen was noticed by Dewar;* and further details were given by myself 
in a short paper published a few years ago.t There I obtained a resistance of 
1*518 for fully-saturated hydrogenium, of which the originally pure palladium 
wire had a resistance of unity. In the present inquiry I have easily obtained a 
much greater increase of resistance — such as 1-634, 1*7775, and even as much 
as 1*83. Whether this may be a result of impurities being present in the acid 
which was used as the electrolyte, I cannot say. It may be noted, however, 
that the palladium wire itself was obtained in Paris, and was guaranteed to be 
very pure indeed. 

The main purpose of the present investigation was to study the temperature 
characteristics of the resistance of hydrogen-charged palladium. Throughout 
each series of experiments the same palladium wire was used, the hydrogen 

* Trans. Roy. Soc. Edin., vol. xxvii. t Proe. Roy. Soe. Edin., 1882-83. 

VOL. XXXIII. PART I. 2 A 



172 DR CARGILL G. KNOTT ON THE 

being added in small successive doses. Not till the maximum saturation was 
reached was the wire subjected to any excessive heating, such as is generally 
supposed to be necessary to drive the hydrogen out. The temperature was 
regulated by means of an oil-bath, into which the wire, firmly bound to 
the ends of stout copper rods, dipped along with the thermometer which 
measured the temperature. The heating was applied gently by means of a 
spirit-lamp. 

In the first series of experiments the temperature was raised gradually to 
about 300° C. ; and in these experiments the loss of hydrogen was beautifully 
shown in the manner by which the resistance began to decrease at a temperature 
of about 260° C. A detailed description of two of the dozen experiments made 
will suffice, as all have almost exactly the same characteristics. I quote ver- 
batim from my experimental book, just as the entries were made after the 
completion of the experiment. 

Experiment made on January 27, 1886. 

Resistance of hydrogenium at 10°*2 C. = 93*6 (10~ 2 ohm) 
(the numbers observed are omitted). 

Description of Results. — Up to temperature 175° C, the resistance of hydro- 
genium grows at a steady constant rate = - 203 per degree centigrade; or to that 
temperature 

E=91 ; 4+-203i 

for this particular specimen ; or, more generally, the resistance of a specimen 
of hydrogenium, whose resistance is 1 ohm at 0° C, is given by the formula 

r = l + -00222£. 

The rate of increase then begins to increase slowly till 220° C. is reached. 

From 220° to 260° the resistance remains practically steady, varying 
through a range of 1 in 140 — that is, 07 per cent. 

From 260° to 280° the resistance falls off very rapidly, attaining its maximum 
rate of decrease at 274°. The rate is then -96 approximately. 

At 280° the rate of decrease markedly diminishes, and seems to tend to 
evanescence till the highest temperature (295°) is reached. 

From this temperature down again to the ordinary atmospheric temperature 
the resistance diminishes at a steady and almost constant rate, namely, 202 per 
degree centigrade ; or 

E= 63-56 + -202 1 
or, reduced as above, 

r=l+-00318*. 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 173 

It is striking that the rates of change of the palladium in its two states are 
such that their total changes through a large range of temperature are the 
same. 

Experiment of February 4, 1886. 

Resistance of hydrogenium at 7° C. = 119*3 (10~ 2 ohm). 

Heating Curve — 

From 0° to 140° dR/dt = -194 , 
and 

R = 118 +194*, 
or 

r = 1 +-00165*. 

From 140° to 260°, the resistance grows to a maximum, such that dRjdt 
changes continuously, increasing to a maximum (*385) at temperature 
225° ±5°, and then diminishing to zero. 

At 260° dR/dt changes sign and continues to increase numerically very 
rapidly, so that at 300° the resistance has fallen from 282*5 to 136. This 
means a very rapid rate of change at about 295°, approximately equal 
to 5. 

The cooling curve gives, as average value, 

dR/dt = -219 
and 

R = 66-5 + -219 t , 
or 

r = 1 + '0033 t. 

These descriptions, with the accompanying curves (A) on Plate XL, are 
sufficient to bring out the peculiarities of the case. The various experiments, 
made with wires of different charge, gave very similar results. From these it 
appears that, up to a temperature of 150° C, hydrogenium of all degrees of 
charge behaves like palladium, except that the temperature-coefficient is 
generally, and always for the higher charges, smaller than for pure palladium. 
At higher temperatures the resistance seems to grow at a more rapid rate, and 
this peculiarity is more marked for the more highly charged metal. This is shown 
also in the fact that the difference between the lowest and highest resistances is 
greater for the more strongly hydrogenised wire. A little above 200°C, the 
hydrogen begins to escape, the first effect being that the resistance increases 
more and more slowly till it reaches a maximum. Diminution of resistance 
then sets in, sometimes with great rapidity, so that before 300° is reached the 
resistance has fallen nearly, if not quite, to what its value would be at that 
temperature for the original palladium. The rate at which this diminution 



174 DR CARGILL G. KNOTT ON THE 

sets in is of course a function of the time as well as of the temperature. I 
believe that, if the wire were kept at a steady temperature of 260°, or even 
lower, it would ultimately lose all its hydrogen. Observations on the 
change of resistance give, indeed, the most delicate means of studying the 
manner in which the hydrogen escapes, and would well repay a careful investi- 
gation. 

These earlier experiments were made with a view to establish the broad 
features of the case. They suggested, however, various lines of further and 
more careful inquiry, of which one has just been mentioned. Another is 
obviously a following up of the remark made at the end of the description of 
the experiment of 27th January, which was indeed the very first of the series. 
The problem, expressed in its generality, is, What relation, if any, exists 
between the temperature-coefficient of resistance and the charge of hydrogen 
present ? At first sight there is a tendency for the total change for a given rise 
of temperature to remain the same whatever charge of hydrogen is present. 
That is if we use throughout the whole series of experiments the same wire at 
different saturations, and draw curves of the resistance (as measured) in terms 
of the temperature, we shall obtain a family of curves which in their initial 
portions run parallel to each other, the lowest curve being that of pure 
palladium, the highest that of saturated hydrogenium. A closer study of the 
various experiments showed that this relation did not strictly hold ; but before 
anything definite could be obtained, it was necessary to make a series of careful 
experiments with this special object in view. The results of these later 
experiments I shall now give, comparing them when possible with the results 
of the earlier series. 

A palladium wire was taken of resistance - 927 ohms at 18° C. Its 
resistances at different temperatures up to 110° or so were carefully measured 
in an ordinary Wheatstone bridge. It was then charged with a small charge of 
hydrogen, and the same process of measurement of resistance gone through, 
and so on, with necessary additions of hydrogen, till the wire became saturated 
with the gas. 

From the observations, the values of the resistance for each wire were 
interpolated so as to correspond to the temperatures 18°, 28°, 38°, &c. The 
subjoined table gives these interpolated values for six different hydrogeniums 
besides the pure palladium itself. In one experiment four terms only appear. 
This resulted from the breaking of the large glass beaker in which the wire 
was being heated : — 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 



175 



Table showing Resistances in Ohms at various Temperatures of Palladium and Hydrogenium. 



Temperature. 


Palladium. 


I. 


II. 


III. 


IV. 


V. 


VI. 


18° C. 


•927 


•991 


1-051 


1-175 


1-306 


1-402 


1-514 


28° 


•958 


1-027 


1-089 


1-207 


1-342 


1-430 


1-547 


38° 


•990 


1-062 


1-123 


1-242 


1-376 


1-464 


1-578 


48° 


1-022 


1-098 


1-157 


1-273 


1-410 


1-497 


1-611 


58° 


1-053 


1-134 


1-190 


1-309 




1-530 


1-645 


68° 


1-084 


1-171 


1-225 


1-346 




1-563 


1-677 


78° 


1-116 


1-208 


1-260 


1-381 




1-597 


1-712 


88° 


1-147 


1-244 


1-296 


1-418 




1-632 


1-746 


98° 


1-176 


1-279 




1-453 




1-669 


1-780 


108° 


1-206 






1-491 




1-700 


1-813 


118° 














1-847 



If a table of first differences is formed from these numbers, it will be found 
that all the hydrogeniums have the first difference nearly constant throughout, 
whereas in the palladium itself the first difference distinctly diminishes as the 
temperature rises. 

The following table gives the mean of the successive differences for each 
specimen : — 



Palladium. 


I. 


II. 


III. 


IV. 


V. 


VI 


•030 


•036 


•035 


•035 


•035' 


•033 


•033 



The gradual decrease in the values for the hydrogeniums as the charge of 
hydrogen increases is so regular, that it is difficult to regard it as accidental. 
Also the distinctly smaller value for the pure palladium is a significant fact ; 
although it must be remembered that it is a mean of a series of steadily 
diminishing values, whose greatest value is nearly -032. The others again are, 
as already pointed out, means of values which must be regarded as practically 
constant throughout the whole range. 

The quantity, however, which should receive our closest attention is, as I 
have pointed out in my previous paper on the resistance of nickel at high 
temperatures, not dKjdt, but 'R~ 1 dR/dt. It will be sufficient at present to 
form this quantity from the series of first differences, by dividing each by the 
mean of the resistances whose difference it is. The sanction for this simple 
mode is the " straight-linedness " of the numbers throughout. The following 
table shows these " logarithm-rates " arranged opposite the interpolated means 
of the temperatures of former table of resistances : — 



176 



DR CARGILL G. KNOTT ON THE 

Table showing the Values at different Temperatures of the "Logarithm Rate" (R~ 1 dR/dt) 

for Palladium and Hydrogenium. 

(For convenience of tabulating, the numbers are multiplied by 10 4 .) 



Temperature. 


Palladium. 


I. 


II. 


III. 


IV. 


V. 


VI. 


23° C. 


34 


36 


35 


27 


28 


20 


21 


33° 


33 


33 


31 


28 


25 


23 


20 


43° 


32 


33 


30 


25 


24 


22 


21 


53° 


30 


33 


28 


28 




22 


21 


63° 


29 


32 


29 


28 




22 


19 


73° 


30 


31 


28 


25 




21 


21 


83° 


27 


30 


29 


27 




22 


20 


93° 


25 


27 




25 




22 


19 


103° 


25 






26 




19 


18 


113° 














18 



If means are taken for the first three numbers in all the columns, and then 
means of the next four, a condensed table will be obtained, which may be 
regarded as giving fairly approximate values for the logarithm rates at tempera- 
tures 33° and 68° These are as follows : — 





Mean Values of t= — — at 
R dt 


33° 


68° 


Palladium, . . 

Hydrogenium I. 

II. 

III. 

IV. 

V. 

VI. 


33 
34 
32 
27 
26 
22 
21 


29 
32 

28 
27 

22 

20 



These numbers bring out very clearly the fact that the first effect of adding 
hydrogen to palladium is to make the resistance of the wire somewhat more 
sensitive to changes of temperature, but that this greater sensitiveness soon 
disappears as more and more hydrogen is added. In the saturated condition, 
hydrogenium resembles other alloys in having a temperature-coefficient for 
change of resistance which is less than for pure metals. 

This conclusion regarding the first effect of adding hydrogen is borne out by 
the results of the earlier series of experiments, which, though not having the 
same claims to accuracy, are now given for purposes of comparison. In the 
columns headed R//R are tabulated the ratios of the hydrogenium wire 
resistances to the resistance of the wire in its pure palladium condition ; and in 
the columns headed a'ja are tabulated the ratios of the corresponding tempera- 
ture coefficients as given by the formula 

R' fl = R'(l+a0), 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 



177 



where 6 is the temperature measured in degrees of the centigrade scale — the 
zero of temperature reckoning being the temperature at which E' is the 
resistance. In the earlier experiments this zero of reckoning is the centigrade 
zero ; in the later experiments 33° and 68° C. 



Comparison of Temperature Coefficients for different Specimens of Hydrogenium. 



Earlier Series. 




Later Series. 




0°C. 


33 


°C. 68° 


C. 


R'/R 


a'/a 


R'/R 


a'/a 


R'/R 


a'/a 


1-06 


1-09 










1-08 


1-06 


1-07 


1-03 


1-08 


i-'io 


1-14 


1-02 


1-13 


•97 


1-13 


•97 


1-17 


1-00 


1-26 


•82 


1-24 


•93 


1-39 




1-39 


•79 






1-47 


"■72 


1-48 


•67 


1-44 


'•76 


1-56 


•76 


1-6 


•64 


1-55 


•69 


1-78 


•50 











The most curious point established in these experiments seems to be that, 
to a fair approximation, the total change of resistance in a given palladium 
wire charged with hydrogen, due to a given change of temperature, is inde- 
pendent of the amount of hydrogen present. Thus, if we form the product 
of each pair of corresponding ratios in the table just given, we shall obtain 
for each column a series of values differing in no case from their mean 
by more than 6 or 8 per cent., with the single exception of the last pair 
in the first column. These means are respectively 111, 107, and 1*12. It 
is not unity, so that the pure palladium does not quite fall in with the hydro- 
geniums. 

Another mode of expressing the fact here indicated is to say that, at any 
temperature below 150° C, the increase in resistance of a given palladium wire 
is a function simply of the amount of hydrogen taken in. This mode of regard- 
ing the phenomenon suggested the inquiry, Does the rate of in-take of hydro- 
gen, or the total amount that can be absorbed, depend upon the temperature 
of the electrolyte ? A direct experiment was tried by connecting two electro- 
lytic cells in series with the source of current, and using, as negative electrodes 
in these cells, two equal portions of the same palladium wire. The liquid in 
the one cell was kept at a steady temperature of 90° C, while the other was at 
the ordinary temperature of the room, about 18° C. No difference, however, 
in the rates of charging, or in the final charge, was observed. . 

The peculiarity in the change of resistance above 150° C, and below the 
temperature at which loss of hydrogen sets in, is reserved for a further dis- 
cussion ; that is, if further experiments reveal anything new. The nature of 



178 



DR CARGILL G. KNOTT ON THE 



the peculiarity is indicated in the curves, and has been already sufficiently 
touched upon. 



The Thermoelectric Properties of Hydrogenium. 

So far as I am aware, this subject has never been attacked by any experi- 
menter. My first inquiry was, therefore, merely as to the existence of a 
thermoelectric current between pure palladium and hydrogenised palladium. 
I quite expected to find such a current, but was very much surprised at its 
magnitude. I cannot do better than quote the whole of the first experiment 
from my experimental book. 

Resistance of palladium wire before hydrogenisation — 

= '64 ohms. 
Resistance of same wire after hydrogenisation — 

= -99 ohms. 

The hydrogenium was then bound to a palladium wire, put in circuit with a 
galvanometer, and the palladium-hydrogenium junction gradually heated in oil 
up to 300° C, and then allowed to cool. The galvanometer was then gauged 
by means of a standard Daniell, whose electromotive force was assumed to be 
1-1 volts. 

The temperatures, with the corresponding deflections, as given in the 
galvanometer scale, are as follows. The cold junction varied from 6°2 to 8° C. 
throughout the experiment : — 



Heating. 



Temperature. 


Deflection 


38° C. 


29-3 


67° 


66 


96°-5 


95-5 


121° 


126 


150° 


159 


182° 


183 


200° 


213 


220° 


222 


235° 


224 


240° 


229 


245° 


220 


250° 


220 


255° 


218 


260° 


218 


265° 


220 


270° 


220 


280° 


219 


285° 


218 


290° 


214 


295° 


220 


300° 


218 



Cooling. 



Temperature. 


Deflection 


300° C. 


218 


295° 


191 


290° 


185 


285° 


179 


280° 


171 


275° 


167 


270° 


161 


265° 


157 


260° 


149 


255° 


145 


250° 


138 ' 


240° 


130 


235° 


125 


230° 


122 


220° 


111 


210° 


101 


200° 


94 


175° 


80 


170° 


75 


155° 


71 


120° 


56 


90° 


40 



(1) 


de 

^ = 1853 

dt 


(2) 


*= 785 

dt 


(3) 


de = 

dt 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 179 

From these numbers the following facts were deduced : — 
If e is the electromotive force expressed in volts, and t the temperature in 
degrees centigrade, it is found that — 
Up to 200° C, temperature rising, 

e= T67xl0- 5 x l"ll(*-8). 

From 200° to 300° C, e is practically steady. 
From 300° to 200°, temperature falling, 

e = 1-67 xl0" 5 (- 105-5 + '945*+ -000313* 2 ). 
From 200° to temperature of air, 

e = 1-67 xlO" 5 x -47(*-6). 
Hence we find, in C.G.S. units, 

from 0° to 200° C. beating, 
from 200° to 0° C. cooling, 
from 200° to 300° C. heating. 

(4) $ = 1578 + 1-044* from 300° to 200° C. cooling. 
dt 

Finally, assuming the palladium to be the same as that investigated by 
Tait, we find for the thermoelectric powers of hydrogenium, in conditions (1) 
and (2), referred to lead (as in Evekett's Units and Physical Constants*) the 

expressions — 

(1) # = 1128 -3*59*. 

(2) p= 160-3-59*. 

Hence, on the thermoelectric diagram the hydrogenium line is something 
like this. It begins near the iron line, runs parallel to the palladium line till 
200° C. is reached, when it falls somewhat quickly to the palladium line, which 
it hugs up to 300° C. During cooling, it seems to start from the point it 
would have occupied had its course remained unchanged during the whole 
heating. From thence it runs at a less inclination than the palladium line 
until the temperature of 200° C. is reached, after which it remains parallel to 
the palladium line down to ordinary temperatures, and comes out a little 
below copper at 0° C. 

Adopting Tait's values as given by Everett for iron, copper, and 

* The signs are here changed so as to agree with Tait's theory, which connects the inclinations of 
the thermoelectric lines with the Thomson effects in the corresponding metals. I shall always speak of 
iron as lying above lead, and palladium as below lead, on the thermoelectric diagram. 

VOL. XXXIII. PART I. 2 B 



180 DR CARGILL G. KNOTT OX THE 

palladium, we may indicate the peculiarities of the hydrogenium by means of 
the following table of thermoelectric powers (t in centigrade degrees) : — 

Iron, 1734- 4-87^ 

Copper, 136+ -95* 

Palladium, - 625 - 3*59* 

Hydrogenium ( 0° - 200°), + 1128 - 3-59* 

(200° -300°), - 625-3-59* 

ii (300° -200°), +1578-2-55* 

(200°- 0"), + 160-3-59* 

It must be understood, of course, that these equations do not strictly hold 
at these temperatures which separate the one group from the other ; at these 
points there are continuous although rapid transitions which baffle an arithmetic 
representation. 

The peculiarities here indicated may be explained as due to the escape of 
the hydrogen during the heating and to its partial return during the cooling. 
Only the one extremity of the hydrogen- charged wire is heated, so that only 
from that portion will the hydrogen escape to any marked extent. Whether it 
escapes wholly out of the wire, or is partly driven into the contiguous colder 
portions, is not certain. The latter possibility is far from improbable, if the wire 
is undercharged to begin with. Whatever may be the case, however, it is 
obvious that at about 200° C. the portion of wire immersed in the hot oil begins 
to lose its occluded hydrogen. The thermoelectric system that now exists is of 
such a complicated nature that it would be difficult, perhaps impossible, to 
predict what should happen. There is a pure palladium wire joined in circuit 
with a hydrogenised palladium wire, whose charge as well as temperature 
varies continuously from the one extremity to the other. Supposing, as I shall 
establish later, that the thermoelectric position of hydrogenium is a function 
of the charge, we have to do with a chain of elements of continuously varying 
thermoelectric power. Adding to this the further complication that there is a 
time variation of both temperature and charge, we can scarcely expect to be 
able to prejudge the phenomenon. The mere fact of a variation of charge may 
— for ought we know to the contrary — bring into play an electromotive force 
of other than purely thermal origin. As the heating changes to cooling, the 
electromotive force which had remained so constant since 200° begins to fall 
away rapidly, but with diminishing rapidity as the temperature falls. There 
certainly seems to be an instability in the condition of the hydrogen during this 
cooling process, for just as the temperature below which hydrogenium was 
stable during the heating the thermoelectric properties recover their original 
ordinary characteristics. The final position of the hydrogenium line, after the 
cooling, shows that there has been a loss of hydrogen at the junction ; but, as 
was proved by resistance measurement afterwards, a very small amount of 
hydrogen was lost to the wire as a whole — not more than 5 or 6 per cent. 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 



181 



The thermoelectric power of the palladium and hydrogenium couple, as 
shown by this first experiment, was so large as to suggest investigating the 
properties of the hydrogenium by coupling it with some other metal, such as 
platinum or copper. The use of the palladium itself is besides open to the 
possible objection that the passage of a current between it and hydrogenium 
may cause a transfer of hydrogen. There was, however, no positive evidence 
of such a possibility. 

In the next experiments to be described a triple junction was formed of 
platinum, palladium, and hydrogenium. Rapidly alternating readings were 
taken of the platinum-palladium and platinum-hydrogenium electromotive 
forces, which were estimated in C.G.S. units. In this way the hydrogenium 
and palladium were directly compared. The following are the results of one of 
the experiments, the same wire being used as in the experiment already 
described. By the addition of a little more hydrogen the resistance was raised 
to 1-012 ohms. 



Comparison of Electromotive Forces of Palladium (P£-Pd) and Platinum- 
Hydrogenium (Pt-Hd) at different Temperatures. 

The numbers are given in 10~ 4 of the C.G.S. units. 



Heating. 



Vt-¥d. 


7t-B.d. 


+ -19 


- -56 


2-06 


- 3-36 


5-57 


- 6-82 


9-51 


- 10-86 


11-9 


-10-7 


12 


- 9-33 


18-5 


- 7-4 


23 


+ -9 


27-5 


+ 8-26 


50 


31-3 


62-1 


41-3 


66-7 


47-2 


81-6 


61-7 


86-1 


67-9 


98-5 


77 


103-9 


82 


114-7 


95-2 


122-5 


102-3 



¥t-~Bd. 



Cooling. 



Ft-Rd. 



122-5 


102-3 


120-1 


98-5 


117-6 


94-8 


108-1 


90-3 


99-4 


84-5 


93-7 


79-6 


89 


74-2 


75-6 


62-5 


60-7 


48-6 


57-6 


46 


54-5 


43-7 


41-8 


32-7 


37-2 


29-8 


34-1 


27 


32-6 


25-4 


28-2 


21-5 


25-5 


20 


19-5 


14-9 


17-4 


13-5 


11-9 


9-3 


8-3 


6-1 



In this experiment the triple junction was enclosed in a small porcelain tube 
and heated in a charcoal furnace. The temperature of 200° C. corresponds 
approximately to the value 16 in Vt-Vd column, and temperature 300° C. to the 



182 DR CARGILL G. KNOTT ON THE 

value 25. The curves marked B in Plate XI. bring out the peculiarities to the 
eye. 

If we try to trace the hydrogenium line on the thermoelectric diagram from 
this curve, we shall get rather a curious result, which is shown roughly in the 
small diagram (C) in the upper left-hand corner of Plate XI. A glance at the 
electromotive force curve indicates, indeed, that the ratio of the thermoelectric 
powers of hydrogenium and palladium referred to platinum begins with a 
negative value greater than unity, passes through zero at about 150° C, becomes 
equal to positive unity at about 200° C, and attains a value greater than unity 
as the temperature passes through 300° C. This may be explained in two 
ways. It may be due to an electromotive force other than thermal, brought 
into existence by the variation of charge or a possible convection of hydrogen 
along the wire. Or, it may be due to the integral electromotive force of a row 
of hydrogenium elements of varying charge and temperature being a function 
of the space-rate of either variation. Ultimately the ratio of the thermoelectric 
powers becomes a little less than unity, and continues so until the temperature 
reaches its highest value. The cooling curve belongs to a diagram line which 
lies between palladium and platinum, dividing the space in the ratio of 
1 to 4. The main features are identical with those of the first experiment, 
the differences in detail being the result of the much higher temperatures 
employed, in virtue of which more hydrogen is lost to the wire. In the 
small thermoelectric diagram the palladium line is drawn parallel to the 
platinum line, although they are really inclined at an angle which would 
make them meet at a point corresponding to - 600° C. The irregularities 
due to the instability of the hydrogen appear in the thermoelectric ex- 
periments at a lower temperature than in the resistance experiments. This 
may well be due to the inequality of temperature distribution along the wire 
in the former case. 

It now remained to make a study of the thermoelectric properties of 
hydrogeniums of intermediate charges. The object aimed at was to obtain 
careful determinations at temperatures below those at which arise the irregu- 
larities due to the instability of the hydrogen. I confined myself, therefore, to 
temperatures below 100° C. The arrangement and reduction of results, which 
present some novelties of operation, were as follows : — 

A triple junction of platinum, pure palladium, and hydrogenium was im- 
mersed in oil, along with a centigrade thermometer, which, however, was used 
rather as an indicator than an accurate measurer. The platinum-palladium 
circuit was indeed the real thermometer ; and in terms of its electromotive 
force the electromotive force of the platinum-hydrogenium circuit was obtained. 
The resistance of each specimen of hydrogenium was measured before and 
after the electromotive force measurements. The mean of these two resistance 



ELECTRICAL PROPERTIES OE HYDROGENISED PALLADIUM. 183 

measurements, which were usually the same, and differed only in one case by 
as much as 1 per cent., may be regarded as a fair indicator of the amount of 
hydrogen present in the particular specimen. The same palladium wire was 
used throughout as the basis for the successive hydrogeniums. 

The resistances were the same in both circuits, so that the galvanometer 
deflections were proportional to the electromotive forces. The circuits could 
be thrown on to the galvanometer in either direction and in rapid alternation. 
The sequence in which the readings were taken was as follows : — Let a, b, sym- 
bolise the readings of the two circuits, and let -I- or — be prefixed to indicate 
the direction in which the current flowed through the galvanometer. Then the 
order in which the observations were made was 

+a— a— 6+6— b—a'+a—a—b+b— 6&c. 

From + a to the next + a represents a complete series, from which two cor- 
responding readings may be obtained ; and similarly from + b to the next + b. 
An example, taken at random from the pages of the experimental book, will 
make the method clear : — 



+a 

161 


(308) 
(325) 


— a 
147 

155 


-6 

164-5 
164-5 


+ 6 
(344-5) 

180 

(344-5) 


171 


(324-5) 


153-5 


170 


(362 ) 

192 



The zero line of the scale lay at the centre, and to this zero the zero position 
of the galvanometer spot of light was roughly adjusted. Hence the sum 
161 + 147 ( = 308) is to a first approximation double the deflection due to the 
average current during the time taken to make the two readings; and similarly 
for all the other successive pairs of readings belonging to either circuit. The 
bracketed numbers show these sums, no two of which are of course simul- 
taneous or correspond exactly to the same temperature. But let us take any 
four in chronological order, such that the first and last belong to one circuit! 
and the two intermediate ones to the other. Then we may assume, if the rate 
of change is slow, that the sums of these pairs are proportional to electromotive 
forces which correspond to the same temperature. In the example given, two 
pairs of corresponding numbers may be obtained by simply adding successive 
pairs of bracketed numbers of the same name, namely, 634, 689, and 650-5, 
706-5. Every number so finally obtained depends on at least three readings. 
I shall give here a portion of one of the tables containing these reduced num- 



184 



DR CARGILL G. KNOTT ON THE 



bers, together with first differences, and the ratios of corresponding pairs of 
differences — which quantit es were necessary for the final reductions. 

Experiment of May 14, 1886. 

Resistance of Hydrogenium = 1 "4245 Ohms. 



Temperature. 


Ft - FLd. 


Differences. 


P^ - Fd. 


Differences. 


Ratio. 




63 




164 










23 




49 


•47 


40° 


86 




213 










23 




50 


•46 




109 




263 










19 




51-5 


•37 




128 




314-5 






50° 


153 


25 


365-5 


61 


•49 






21 




55 


•38 


60° 


174 




420-5 







and so on. 

The temperatures in the first column are not to be regarded as accurately 
determined. They merely indicate, to a sufficient approximation, the tempera- 
ture of the moment. The ratios in the last column should give the ratios of 
the corresponding electromotive powers of hydrogenium and palladium referred 
to platinum. The mean of all for any one experiment will give a good value for 
this ratio at the mean temperature of 60° C, the cold junction being 20° C, 
and the highest temperature being 100° C. Instead of taking a single mean, 
however, I divided the experiment into two portions, and found the mean of 
all differences below 80° C. and the mean of all differences above 80° C. In 
this way I got two values for the ratio — one corresponding to temperature 
50° C, and the other to temperature 90° C. These ratios, which are repre- 
sented by the symbol de'/de, are given in the accompanying table, each 
specimen of hydrogenium being distinguished by its resistance estimated in 
terms of the resistance of the originally pure palladium wire ; that is, by the 
ratio B'/R 



Table comparing the Changes in Resistance and in Thermoelectric Power of Palladium Wire charged 

with different amounts of Hydrogen. 



R'/R 


1 


1-043 1-121 


M89 


1-26 


1-302 


1-395 


1-504 


1-78 


de l de \ 90° 


1 
1 


•88 
•88 


•75 
•76 


•77 
■70 


■70 
•65 


•63 

•61 


•47 
•53 


•44 
•44 


-1-58 
-1-58 


'/- ' 'de (mean) 


1 


•88 


•755 


•735 


•675 


•62 


•50 


•44 


-1-55 



ELECTRICAL PROPERTIES OF HYDROGENISED PALLADIUM. 185 

These numbers prove two things — 

1. The greater the charge of hydrogen, the higher on the thermoelectric 

diagram is the hydrogenium line. 

2. The displacement of the line for a given increment of charge is 

greater at the higher charges. 

So striking is this second peculiarity that, whereas it requires the resistance 
of the wire to be increased by 50 per cent., so as to bring the line half way to 
the platinum line, it requires only 78 per cent, to make it move to the other 
side of the platinum line to a distance greater by 50 per cent, than the distance 
of the palladium line. This is indicated by the figures in the last column having 
a negative sign. The great displacement in the hydrogenium line at high 
charges, as proved by these experiments, is in agreement with the results of the 
earlier experiments. 

It does not seem possible to draw any conclusion from the values given as 
to there being any change in the inclination of the hydrogenium line. The 
safest conclusion to draw would be that, on the whole, the ratio de'jde remains 
constant through the corresponding range of temperature — that is, through 
40° C. If this were so, it would mean that the hydrogenium line is not parallel 
to the palladium line, since the latter is itself inclined to the platinum line. 
The thermoelectric powers of palladium to platinum at 50° C. and 90° C. are in 
the ratio of 70/75. If the hydrogenium line were parallel to the palladium line, 
the corresponding ratio for it would be smaller for all the cases studied except 
the last, for which it would be greater, being indeed greater than unity. There 
is certainly no indication of such a property in the tabulated numbers. The 
properties are indeed almost reversed. 

Again, the constancy of the ratio de'jde for all temperatures (if surely 
established) would mean that the hydrogenium lines all pass through the point 
of intersection of the palladium and platinum — a very remarkable fact, should 
it be established by later experiments. We might then reason as to the 
existence of a hydrogen line passing through the same point. Certainly the 
constancy of this ratio is well marked in the last two cases, just the ones where, 
upon the very natural hypothesis of parallelism, it should be most distinctly 
variable. A closer study of the subject seems called for, and I hope before 
long to attack the problem in a somewhat different manner. It may be said 
that we can hardly expect to avoid irregularities due to a probable inequality 
in the distribution of the hydrogen charge. Such irregularities will obviously 
have more effect in thermoelectric measurements than in resistance measure- 
ments. 

In connection with the subject of the thermoelectric properties of hydro- 
genium, the following will make an instructive lecture experiment. A palladium 



186 DR CARGILL G. KNOTT ON THE ELECTRICAL PROPERTIES, ETC. 

wire is hydrogenised throughout half its length, and its extremities attached to 
the terminals of a galvanometer. If, now, a flame is applied to the centre of 
this apparently single uniform wire, a large thermoelectric current is obtained, 
which grows to a maximum and then falls down to zero. This spurious neutral 
point is of course simply the result of hydrogen being lost to the heated portion. 
As the wire cools down again no such large current is obtained. The effect 
may be reproduced a number of times by following up with the flame the ever- 
shifting point of separation of the hydrogenium and the palladium. 

Summary. 

The electrical resistance of hydrogenium increases with the temperature up 
to the point at which hydrogen begins to be given off. Thereafter the resistance 
begins to decrease till all the hydrogen has been driven away, after which 
increase sets in again as the now pure palladium wire is heated. The tempera- 
ture-coefficient diminishes as the charge increases, and in such a manner that 
the total increase of resistance through a given range of temperature is nearly 
the same for the same palladium wire whatever the charge may be. In other 
words, at any given temperature below 150° C, the increase of resistance due 
to a given additional charge is the same. The changes of resistance between 
200° C. and 300° C. afford a very delicate means of studying the manner in 
which the hydrogen escapes. 

The thermoelectric current in a palladium-hydrogenium circuit flows from 
palladium to hydrogenium through the hot junction — that is, the hydrogenium 
line lies higher in the thermoelectric diagram than the palladium line. The 
higher the charge the higher the position. Saturated hydrogenium lies, for 
ordinary atmospheric temperatures, between copper and iron. Up to 150° C. 
the hydrogenium lines are straight lines, and nearly if not quite parallel to the 
palladium line. Above 200° C. rapid changes set in, the result no doubt of the 
loss of hydrogen at the junction. On cooling, the hydrogen seems to return 
partially to the extremity from which it has been driven. The effects at high 
temperatures are, however, complicated, because of the unequal distribution of 
hydrogen in the palladium. 



Vol. xxxin. pi. xi. 




;Wcliibalxt ft Peck Eng r . s Edin' 



( 187 ) 



VIII. — The Electrical Resistance of Nickel at High Temperatures. By 
Cargill G. Knott, D.Sc. (Edin.), F.RS.E., Professor of Physics, 
Imperial University, Tokayo, Japan. (Plate XII.) 

(Read 5th July 1886.) 

In the Proceedings of the Royal Society of Edinburgh for 1874-75 there is a 
short paper on the "Electrical Resistance of Iron at a High Temperature." 
It is the record of certain experiments made by three of us, then students in 
the Physical Laboratory of the University of Edinburgh ; and its conclusion is 
that there is a peculiarity in the behaviour of iron as an electric conductor 
at the temperature of a dull red heat. At this temperature other physical 
peculiarities are known to exist, particularly as regards its thermal expansion, 
its thermal capacity, and its specific heat for electricity. The discovery 
of these striking properties we owe respectively to Dr Gore,* Professor 
Barrett,! and Professor Tait.J 

Professor Tait's discovery, that the Thomson effect in iron changes sign at 
certain high temperatures, is in itself very striking ; and, when taken in connec- 
tion with other coexistent peculiarities, suggests various lines of inquiry. 
The most obvious is, perhaps, the question as to its occurrence in other metals. 
There is one other metal which rivals iron in thermoelectric eccentricity, namely, 
nickel. At a temperature of 200° centigrade, its Thomson effect gradually 
changes sign from a considerable negative value to a large positive value, 
changing back again to nearly its original value at 300° C. If nickel thus 
agrees with iron in one exceptional feature, it may well be expected to agree 
in others. In short, Does nickel between the temperatures of 200° and 300° C. 
undergo exceptional changes in length ? is there a phenomenon corresponding 
to Barrett's reglow % and has the electric resistance any unusual change at 
these temperatures ? The first and third questions may be readily answered 
by experiment ; the second, however, seems to offer almost insuperable diffi- 
culties as a subject of investigation. The following paper deals with the third 
of these inquiries. 

I have thought it well to embody, along with the results for nickel, corre- 
sponding results for iron. The chief reason for this is, that in the experiments 
conducted in 1874 by Messrs Smith and Macfarlane and myself, only a 

* Proc. Roy. Soc. Edin., 1869, and Phil. Mag., 1869. 
t Phil. Mag., 1873. 
% Trans. Roy. Soc. Edin., 1872-73. 
VOL. XXXIII. PART I. 2 C 



188 DR CARGILL G. KNOTT ON THE 

general qualitative result was obtained. The method adopted was not one 
which lent itself to accurate quantitative determinations, and to obtain such 
is in itself an important quest. Moreover, the ultimate nature of the pecu- 
liarity can only be seen in its true light by a direct comparison of the individual 
characteristics as shown by iron and nickel. The great difficulty in making 
such a comparison arises from the high temperature at which the phenomenon 
shows itself in iron ; and a further complication springs from the change in the 
metal, due to oxidation and tempering. In the case of nickel, however, the 
critical temperature is within reach of a mercurial thermometer, and the 
oxidation is insignificant. It is highly probable, then, that the results for 
nickel will be more definite and unmistakable than those for iron.* 

In the experiments to be described, the resistances were measured by the 
simple form of Wheatstone bridge. The wires were generally tested in pairs, 
necessarily so in the measurements at very high temperatures. Four stout 
copper rods, 60 cm. long, 7 square cm. cross-section, furnished with strong 
shoulder binding screws at the extremities, were fixed in a vertical position 
some little distance apart. Their lower extremities were joined in pairs by two 
wires, one of which was a specimen of nearly pure platinum, and the other the 
nickel, iron, or palladium wire which was being tested. The upper extremities 
of the rods were joined by stout copper wires to a commutator, which was in 
connection with a Wheatstone bridge resistance box of ordinary construc- 
tion. The current was obtained from a gravity Daniell of high resistance ; 
and the measurements were made by means of a dead-beat mirror astatic 
galvanometer constructed by Elliott Brothers. 

The earlier experiments and some of the later ones were carried out by 
Messrs Hirayama and Saneyoshi, two science students in the Imperial 
University, Tokay o, and were originally intended simply as an exercise in 
laboratory work. Two wires, one of nickel and the other of platinum, were 
coiled in long spirals, and fixed to the lower extremities in the manner already 
described. A vessel containing olive oil was then brought into position, so that 
the wires were wholly immersed. The temperature was gradually raised by 
means of a spirit-lamp, and the resistances measured at convenient intervals. 
The temperatures were given by a centigrade thermometer, whose bulb hung 
in the centre between the terminals of the wires. The oil was briskly stirred 
the whole time, so as to secure a practically uniform temperature throughout 
the mass. The thermometer itself was tested directly at freezing and boiling 
points, and the necessary corrections applied. The error being the same at 
both points, it was assumed to apply throughout the whole range of readings. 
Two specimens of nickel wire were studied, which we shall distinguish as the 
thick nickel and the thin nickel. Tables A and B give the observations for 
* See also Proc. Soy. Sac. Edin., ix. 120, 1875-76. [P. G. T.] 



ELECTRICAL RESISTANCE OE NICKEL AT HIGH TEMPERATURES. 189 

these wires ; tables C and D give the corresponding results for platinum and 
palladium. They are added simply for the sake of comparison. 

The first column contains the corrected temperatures ; the second the 
resistances corrected for the connections ; and the third these resistances 
reduced so as to make the resistance at 0° C. equal to 100. The value of the 
resistance of the wire at 0° C. was in all cases calculated — in the case of 
platinum and palladium from the empirical parabolic formula which was found 
to agree well with the observations, and in the case of nickel by the method of 
successive differences from the first five or six numbers. This latter method 
was used because, for the nickel measurements, it was found quite impossible 
to obtain a suitable formula of ascending powers of temperature up even to the 
fourth. The reduced resistances of the third column for each wire are repre- 
sented graphically in their relation to temperatures on Plate XII. (I.). The 
diameters and specific resistances of each wire are given at the head of each 
list of numbers. 

The resistances throughout are measured with greater accuracy than the 
temperatures. In some cases, the temperature being steady, the resistance 
was adjusted by means of a large shunt set in an arc along with the units of the 
resistance box. In other cases — and this was latterly found the more con- 
venient method — the resistance was fixed as near as the coils would allow, and 
the temperature of the wire slowly raised till the current through the galvano- 
meter just vanished. Hence, although the resistances in table A appear only 
to the third significant figure, they are really certain to the fourth. 

Table A. — Thick Nickel. 



Diameter = 


= •05 cm. Specific resistance = 9697 ( 


C.G.S.). 




Resistance of 


Resistance reduced 


Temperature. 


Wire used. 


for comparison. 


0°C. 


■724 ohms 


100 


10° 


•757 


104-6 


20° 


•79 


1091 


29° 


•82 


113-3 


66°-4 


■ 95 


131-2 


88° 


1-03 


142-3 


98°-6 


1-07 


147-8 


114°-6 


1-14 


157-5 


122°-6 


1-17 


1616 


131°-6 


1-21 


167-1 


142°-3 


1-26 


174-0 


167° 


1-37 


189-2 


187° 


1-47 


203-0 


198°-5 


1-53 


211-3 


215° 


1-62 


223-8 


220°.3 


1-65 


227-9 


233° 


1-72 


237-6 


251° 


1-83 


252-8 


255° 


1-85 


255-5 


264°-8 


1-91 


263-8 


267°-5 


1-93 


266-6 



190 



DR CARGILL G. KNOTT ON THE 



Table A. — continued. 

Diameter ='05 cm. Specific resistance = 9697 (C.G.S.). 

n, Resistance of 

lemperature. ,,r. , 

r Wire used. 

278° C. 2-00 ohms 

281° 2-02 

293° 2-10 

295° 2-11 

300° 2-15 

301°-4 2-16 



Resistance reduced 
for comparison. 
276-2 
2790 
290-1 
291-4 
296-7 
298-4 



Table B.—Thin Nickel 



Diameter = -0154 cm. 



Temperature. 

0°C. 
9° 
33°-i 

56°-5 
' 76° 
99° 
120°-4 
143°-7 
165° 
182°-5 
203° 
226° 
248°-8 
266° 
290°-4 
305° 



Specific resistance = 14500 (C.G.S.). 

Resistance of Resistance reduced 

Wire used. for comparison. 

1-914 ohms 100 

1-96 102-4 

2-09 109-2 

2-233 116-6 

2-38 124.3 

2-55 133-2 

2-716 141-9 

2-915 152-3 

3-091 161-5 

3259 170-3 

3-457 180-6 

3-697 193-2 

3-96 206-9 

4-17 217-9 

4-48 2341 

4-73 247-1 



Table C. — Platinum. 



Diameter = -049 cm. 



Temperature. 

0°C. 
35°-5 
58° 
80°-5 
99°-5 
119° 
141°-3 
163°-8 
186°-3 
204° 
22F-3 
243°-l 
261° 
278° 
295°-8 



Specific resistance = 16800 (C.G.S.). 
Resistance of Resistance reduced 

Wire used. for comparison. 

1-02 ohms 100 

1-11 108-8 

1-164 114-1 

1-208 118-4 

1-256 123-1 

1-30 127-5 

1-35 132-4 

1-40 137-3 

1-45 142-2 

1-484 145-5 

1-523 149-4 

1-58 154-9 

1-612 158-0 

1-642 161-0 

1-69 165-7 



Temperature. 

0°C. 

9° 
31* 
56° 



Table D. — Palladium. 
Diameter = 0396 cm. Specific resistance = 10680 (C.G.S.). 

Resistance of Resistance reduced 

Wire used. for comparison. 

1-595 ohms. 100 

1-64 102-8 

1-77 111-0 

1-914 120-0 



ELECTRICAL RESISTANCE OF NICKEL AT HIGH TEMPERATURES. 

Table D. — continued. 
Diameter = -0396 cm. Specific resistance = 10680 (C.G.S.). 

Resistance of Resistance reduced 



191 



Temperature 


76°-5 C. 


99° 


120°-4 


144° 


165° 


184°-5 


204° 


226° 


247° 


268°-5 


291°-5 


305° 



Wire used. 
2-02 ohms 
2-146 
2-265. 
2-39 
2-508. 
2-607 
2-72 
2-832 
2-94 
305 
3-163 
3-216 



for comparison. 
126-7 
134-6 
142-0 
149-9 
157-3 
163-5 
170-5 
177-6 
184-4 
191-2 
198-3 
201-3 



A glance at the columns of reduced resistances, or at the representative 
curves, shows at once one peculiarity of nickel as compared with the other 
metals, namely, the comparatively great increase of resistance throughout the 
measured range of temperature. The curves further show, by the manner of 
their curvature, that the rate of increase of resistance of a given nickel wire per 
degree centigrade increases as the temperature rises ; whereas this rate of in- 
crease diminishes in the case of platinum and palladium. The same fact is readily 
shown from the numbers themselves by dividing the successive first differences 
of either column of resistances by the corresponding temperature differences. 

The impossibility of representing the march of the nickel resistance by an 
empirical formula of ascending powers of the temperature has been already 
noticed. Some mode of formulating the results is, however, advisable, so as to 
make them numerically comparable with the results for platinum and palladium, 
which can be represented very approximately in the usual way. The following 
mode seems to be in many respects suitable : — 

First, calculate by strict interpolation methods from five contiguous observa- 
tions, the resistances corresponding to successive conveniently chosen tempera- 
tures, say, 0°, 50°, 100°, 150°, 200°, and 250°. Then tabulate, as in the sub- 
joined table, the successive differences of these resistances. In the series of 
2nd differences we recognise at once the impossibility of applying a parabolic 
equation to the results for nickel. 

Table of Successive Differences of Thick Nickel Resistances. 



Temperature. 


Resistance. 


1st Differences. 


2nd Differences. 


0° 


•724 


-168 




50° 


•892 


-184 


-016 


100° 


1-076 


-219 


-035 


150° 


1-295 


-243 


-024 


200° 


1-538 


-287 


-044 


250° - 


1-825 




. „ _ 



192 DR CARGILL G. KNOTT ON THE 

Table of Successive Differences of Thin Nickel Resistances. 

Temperature. Resistance. 1st Differences. 2nd Differences. 

0' 1-914 

• 275 

50° 2-189 -091 

-366 

100° 2-555 -045 

-411 

150° 2-966 -050 

-461 

200° 3-427 -084 

•545 
250° 3-972 

Although it is impossible to get a single parabolic equation to apply all 
through, we may calculate parabolic equations to apply to successive over- 
lapping, segments of a hundred degrees' range, taking as initial points the 
successive temperatures 0°, 50°, 100°, 150°. We thus obtain four equations, 
which will be found to agree closely with the observations. To compare these 
equations with those for other metals, such as platinum and palladium, would 
then be an easy matter. 

It is to be remembered, however, that the usual method of representing 
observations by an empirical formula of ascending powers of the one variable 
has rarely any deep significance. What is of real importance in all such 
investigations is to know, first, what the value of a certain quantity is, and, 
second, how it varies under given conditions ; and in many instances the latter 
is the main object of research. It is so in the present inquiry. It should be 
our object, then, to tabulate our results in such a manner that the rate of change 
of resistance per degree of temperature may be evident at a glance for all tem- 
peratures. The usual equation is of the form 

R = Ro(l + at +/3t 2 ), 

from which we may almost at once calculate dH/dt for any temperature. 

What we wish, however, is not so much this quantity as the quantity 'R- 1 dR/dt, 

which is the real rate of change of resistance. 

In the following table this quantity is calculated for the four series of 

observations already given, so that the peculiarities of nickel may be readily 

indicated. The quantities are estimated for the temperatures 50°, 100°, 150°, 

200°, since for these alone can be safely estimated the rates of change in the 

case of the nickel. The necessary calculation is most readily effected by means 

of the formula — 

1 dR, 1 A 



li, dt " ll t ~\ 



where Ax A 2 are the first and second differences in the series of resistances, 



ELECTRICAL RESISTANCE OF NICKEL AT HIGH TEMPERATURES. 193 

corresponding to the temperatures t-r, t, t + r. The values for platinum and 
palladium are similarly estimated. 



Temperature. 


XT A t l dJil f 

Valuesof R* Tt for 


Thick Nickel. 


Thin Nickel. 


Platinum. 


Palladium. 


50° C. 
100° 
150° 
200° 


•00395 
•00375 
•00357 
•00342 


•00293 
•00306 
•00294 
•00294 


•00218 
•00198 
•00170 
•00142 


•00302 
•00249 
•00225 
•00197 



This table shows very distinctly the real nature of the difference between 
nickel and the other two metals ; it is a difference only of degree. The quan- 
tity R^dH/dt or d log ~R/dt, we shall, for brevity's sake, call the logarithm rate, 
per unit rise of temperature being understood. It appears, then, that nickel 
differs from platinum or palladium, or most other metals, in the fact that its 
logarithm rate does not change so much with rise of temperature. In the case 
of the thin nickel, indeed, it is practically constant, so that the march of resist- 
ance with temperature could be very approximately represented by a simple 
logarithmic equation. 

It may be noted that the logarithm rates for platinum and palladium are 

approximately inversely as the corresponding absolute temperatures. Hence 

we have 

_1_ dR_ h_ 

R dt~ 1 

For platinum, k = '7 roughly; 
„ palladium, k = "95 „ 

Integrating and evaluating the constant by the condition 

R = 100 when £ = 274, 

we find, for platinum, the formula 

R = r97x*°- 7 ; 

and, for palladium, 

R = -4'83x* 095 . 



These formulas will be found on trial to be in fair agreement with the numbers 
given in tables C and D. 

We may also by integration of 



1 dR 

R dt 



= -003 



obtain a formula for the thin nickel. Its form is 

Nap. log. (R x -0228) = -003 x t , 



194 DR CARGILL G. KNOTT ON THE 

where t is, as before, the absolute temperature. This expression will likewise 
be found to suit the numbers given in the last column of table B. 

There is no very obvious mode for obtaining a similar formula for the thick 
nickel. 

It may be remarked that this mode of representing the temperature rela- 
tions of resistance by a power of the absolute temperature — a power which may 
be fractional — includes as a special case the well-known statement that, for 
pure metals, the resistance is directly as the absolute temperature. For small 
ranges of temperature the equation 

R = CT* 
may be easily thrown into the approximate form 

where T is absolute temperature, t centigrade, and the other quantities are 
constants. In this case a is to a first approximation equal to k times the 
reciprocal of 274. 

We now pass to the discussion of the second series of experiments. In 
these the temperature was raised to a fairly bright red heat by means of a 
charcoal furnace. The four stout copper rods, with the attached wires which 
were to be tested, dipped into a porcelain vessel through suitable holes in the 
lid. The vessel itself stood inside a small charcoal furnace, and was heated by 
red charcoal dropped in around it. After reaching its highest temperature the 
charcoal and wires gradually cooled; and during this cooling the resistances of 
the two wires were measured in rapid alternation. 

To obtain what might be regarded as simultaneous values of the resistances, 
means of successive pairs of readings for the one metal were interpolated. 
In every case the one wire was the same piece of platinum, whose indications 
served the purpose of a thermometer. In terms of its resistances, the resist- 
ances of the other wires could be expressed, graphically or otherwise. Many 
experiments were made with each kind of wire, and a vast number of observa- 
tions accumulated. These I have not thought necessary to reproduce in the 
form in which they were obtained. The five curves of Plate XII. (II.), however, 
which tell their own tale clearly enough, are drawn from the observations, 
conveniently reduced, of the five best experiments. The reductions were the 
same as those made in the earlier series of experiments ; that is, the resistance 
at 0° C. for each metal was reduced to 100, and the other resistances changed 
proportionally. 

Although the numbers themselves are not reproduced, their essence is 
given in table E, which is really a comparative table of the resistances of 
certain wires at various temperatures from 0° C. to a fairly bright red heat. 
The series of platinum resistances, as shown in the first column, rises from 100 



ELECTEICAL RESISTANCE OP NICKEL AT HIGH TEMPERATURES. 195 

to 230 by successive additions of 10. From the reduced observations in the 
several experiments, the resistance of any metal corresponding to each one of 
the chosen platinum resistances can be readily calculated. Thus the number 
401 in the fourth column means that a piece of thick nickel, whose resistance 
at 0° C. is 100, has a resistance of 401 at that temperature at which 190 is the 
resistance of a piece of platinum whose resistance at 0° C. is also 100. In 
short, the platinum column serves the purpose of a provisional temperature 
scale, in terms of which the resistances of the other metals are expressed. 
Under each column a row of differences is added. These bring out strongly 
the peculiarities which are disclosed by a glance at the curves of Plate XII. 
(II.). On the left of the platinum column a few numbers are given to indicate 
the temperature in degrees centigrade. Above the value 320° C, the estima- 
tion is only approximate, and is based on the assumption that platinum 
wire changes in resistance according to a parabolic function of the tempera- 
ture. 700° C. may be regarded as a fair approximation to the highest tem- 
perature. Besides the nickels and palladium used in the former series of 
experiments, two specimens of iron were investigated, and are given for pur- 
poses of comparison. 



Table E.- 


—Comparison < 


if the Resistances of various Metals at different Temperatures. 


Temp. 
in°C. 


Platinum. 


Palladium. 


Thin Nickel. 


Thick Nickel. 


Iron 


(1). 


Iron 


(2). 




Resist. 


Diff. 


Resist. 


Diff. 


Resist. 


Diff. 


Resist. 


Diff. 


Resist. 


Diff. 


Resist. 


Diff. 




230 


10 


303 


14 


350 


12 


476 


19 


713 


80 


718 


75 


580° 


220 
210 
200 


10 
10 

10 


289 
275 
263 


14 
12 
14 


338 

(325) 

311 


13 
13 
14 


457 
440 
418 


17 

22 
17 


633 
550 

485 


83 
65 
60 


643 

568 
514 


75 
54 
51 


420° 


190 
180 


10 
10 


(249) 
234 


15 
16 


297 
282 


15 
16 


401 
378 


23 
43 


425 
371 


54 
45 


463 

405 


58 
50 


320° 


170 


10 


218 


17 


266 


31 


335 


52 


326 


42 


355 


50 


270° 


160 


10 


201 


17 


235 


29 


283 


43 


284 


42 


305 


44 


220° 


150 


10 


184 


17 


206 


30 


240 


34 


242 


28 


261 


42 


180° 


140 


10 


(167) 


17 


176 


24 


206 


36 


214 


34 


219 


32 


130° 


130 


10 


150 


17 


152 


19 


170 


29 


180 


32 


187 


32 


84° 


120 


10 


133 


17 


133 


15 


141 


21 


148 


27 


155 


28 


40° 


110 


10 


(116) 


16 


(118) 


18 


(120) 


20 


121 


21 


127 


27 


0° 


100 




100 




100 




100 




100 




100 





VOL. XXXIII. PART I. 



2D 



196 DR CARGILL G. KNOTT ON THE 

First, we notice that palladium is very similar to platinum in the manner 
of its changings, tending, however, to diminish in rate of change as compared 
with the platinum at higher temperatures. Secondly, we see at a glance 
that the behaviour of the nickels is very peculiar. About a temperature 
of 180° or 200° C. the rate of growth of resistance of a given wire with 
temperature undergoes a marked increase, and experiences a more evident 
decrease at a temperature somewhat above 300° C. Throughout this range 
of temperature the comparatively great slope in the resistance curve is very 
striking. 

Thirdly, there seems to be a similar increase in the rate of growth of resist- 
ance of iron wire, occurring at a temperature a little below 600° C. It was 
unfortunately impossible to attain a much higher temperature with the means 
at our disposal ; but in the very highest readings obtained there was sometimes 
an indication of a decrease setting in, as in the case of nickel. In the curves 
as drawn the peculiarities of the iron are not very distinctly shown. It was 
thought better, however, to draw the curve to the same scale as the curves for 
the other metals than to proportion the co-ordinates to make it well-conditioned. 
The curves indicate at once the extremely great increase of resistance in 
iron as compared with other metals. This is in accordance with former experi- 
ments ; and the results here obtained agree fairly well with Von Walten- 
hofen's results for steel (see Wiedemann's Electricitdt, vol. i. p. 525). The 
measurements made by other experimenters do not agree nearly so well — as a 
rule, a much smaller increase has been found. # 

In this paper, however, no special emphasis is laid on the results for iron, 
except that they cannot be represented by any ordinary empirical formula, such 
as C. W. Siemens has given. So far as they go, they bear out our result of 
twelve years ago, that the rate of growth in resistance of iron experiences a 
marked increase at a temperature of a dull red heat. This peculiarity has now 
been proved to exist in the case of nickel, occurring however at a much lower 
temperature. The further peculiarity, so distinct in the case of nickel — namely, 
the subsequent decrease in the rate of growth — probably exists also in the case 
of iron. Indeed, on Von Waltenhofen's authority, the continued increase of 
resistance of steel as the temperature rises from a red heat to a white heat 
tends to evanescence. This bears out the statement made above. Thus, it 
appears that iron and nickel agree in a certain peculiarity in the rise of their 
resistance with temperature. This peculiarity may be thus described. Within 
a certain range of temperature, the resistance of a given wire increases at a 
more rapid rate per temperature degree than at temperatures above or below 
this particular range. For nickel this range lies between 200° and 320° centi- 
grade ; for iron between a dull red and a bright red heat. Now, it is exactly 
within these ranges respectively that the thermoelectric peculiarities of nickel 



ELECTRICAL RESISTANCE OF NICKEL AT HIGH TEMPERATURES. 197 

and iron occur. In no other metals have any similar peculiarities been 
observed. Hence we may regard it as an experimental truth that the interesting 
changes in the sign of the Thomson effect in metals in which such changes do 
occur are accompanied by peculiar changes in the manner of growth of resistance 
with temperature. 

In the case of the nickel, the simultaneousness of the two peculiarities was 
demonstrated by direct experiment. In effecting this direct comparison, we 
tried many modifications; but the essential characteristic of the experiment 
was to obtain, alternating with the resistance measurements, accurate deter- 
minations of the electromotive force of a nickel-palladium pair. In some 
cases the measurements of the platinum resistance were used as the tempera- 
ture scale in which to express this electromotive force ; in other cases the 
platinum wire was dispensed with, so far as resistance measurement was con- 
cerned, but was introduced as a third element in the thermoelectric junction, 
after the convenient manner invented by Professor Tait. That is, the three 
wires — nickel, palladium, and platinum — were bound together as a triple junc- 
tion, and the free extremities led off in such a way that the nickel-palladium 
circuit and palladium-platinum circuit could be thrown on to the galvanometer 
in rapid alternation. In this form of experiment the palladium-platinum 
circuit played the rdle of a thermometer. The platinum was very similar 
in its thermoelectric properties to the kind named " Soft Pt " in Professor 
Tait's first approximation to a thermoelectric diagram. Its thermoelectric 
line was but slightly inclined to the palladium line, and the electromotive force 
of the palladium-platinum circuit increased at a somewhat quicker rate than 
the temperature as estimated in centigrade degrees. 

In whatever way the temperature was virtually measured, whether by the 
resistance of platinum or the electromotive force of the palladium-platinum 
circuit, the experiment gave us the means of comparing directly the two 
peculiar effects of nickel. Two curves could be drawn, the one showing the 
march of the electromotive force of nickel-palladium with temperature, the 
other giving the same thing for nickel resistance. The resistance curve was 
similar in all respects to those already shown in Plate XII. (II.) ; the electro- 
motive force curve reproduced with wonderful fidelity the old result of Professor 
Tait. Beginning nearly straight at low temperatures, or if anything slightly 
concave upwards, it became, as the temperature approached 250° C, distinctly 
convex upwards. About 300° C. the neutral point was reached, and shortly 
after passing the vertex the curve became accurately straight, and continued 
so to the highest temperatures. In fact, it consisted practically of two straight 
portions, oppositely inclined to the line of temperatures, and connected by a 
parabolic arc with vertex at 300° C. This, of course, shows that the nickel 
line on the thermoelectric diagram, lying at low temperatures below the 



198 DR CARGILL G. KNOTT ON THE ELECTRICAL RESISTANCE OF NICKEL. 

palladium line,* continues parallel thereto till the temperature reaches 200° C, 
after which it gradually bends up towards the palladium line. This it cuts 
through at the neutral point (300° C), and almost immediately thereafter bends 
round again into parallelism with the palladium line. Now these two rapid 
bendings were found to occur just at the temperatures at which the peculiar 
bendings occurred in the resistance curve. 

Similar experiments were tried on iron, with, however, doubtful results. 
This was certainly in the main due to the non-efficiency of the method of 
preparing and keeping a high temperature. 

The main results of these experiments may be thus described : — 

1. The rate of growth of the resistance of a given nickel wire with 
temperature is greater, on the average, than the corresponding 
quantity for platinum or palladium, and less than that for iron. 
' 2. The " logarithm rate "- — that is, the rate of change per unit rise of 
temperature of unit resistance at any temperature — falls off more 
slowly for nickel as the temperature rises to 200° C. than it does 
for platinum or palladium. 

3. At about 200° C. the rate of resistance-growth for nickel increases 

markedly, and continues practically steady till about 320° C, when 
a sudden decrease occurs, and thereafter the resistance steadily 
increases at this diminished rate. In other words, between the 
limits of temperature specified, the slope of the resistance curve 
is much steeper than for any other temperature. The same pecu- 
liarity is probably possessed by iron between the temperatures of 
a dull red and a bright red heat. 

4. The peculiarity occurs (in each case) between the limits of tempera- 

ture within which the striking thermoelectric peculiarity discovered 
by Tait also occurs — a peculiarity which is quite unknown in the 
case of any other metal. 

5. There is thus a strong presumption that the Thomson effect in 

metals has a close connection with the mutual relations of resist- 
ance and temperature ; at any rate in metals in which the 
Thomson effect is proportional to the absolute temperature (accord- 
ing to Tait's theory), the " logarithm rate " of change of resistance 
seems to be very approximately inversely as the absolute tempera- 
ture. In nickel and iron, in which the law of the Thomson effect 
is peculiar, such a simple relation between resistance and tempera- 
ture does not hold. 

* It is to be regretted that certain writers still persist in turning the diagram, as it were, upside 
down, thus losing the advantage of Tait's improvement on Thomson's original form — an improvement 
which fits in so admirably with the sign of the Thomson effect. 



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( 199 ) 



IX. — The Formation of the Germinal Layers in Teleoslei. By George Brook, 
F.L.S., Lecturer on Comparative Embryology in the University of 
Edinburgh. (Plates XIII.-XV.) 

(Read 1st February 1886.) 

Introduction^ 

A little more than a year ago, I was led to conclude that the primitive 
hypoblast in pelagic Teleostean ova was derived mainly from the unsegmented 
protoplasm forming the floor of the segmentation cavity. In this respect 
my results were mainly in harmony with the researches of Lereboullet (21), 
Kupffer (18 and 19), Klein (16), Van Bambeke (3), and others, but 
opposed to the more recent investigations of Henneguy (10), Hoffmann 
(14), Kingsley and Conn (15), Ryder (24), Agassiz and Whitman (1), and 
Cunningham (8.) At that time I adopted Agassiz and Whitman's name of 
periblast for the subgerminal layer containing free nuclei, though I differed 
from those authors in my idea of the mode of origin of the nuclei. As, how- 
ever, I regard the tissues derived from this layer as belonging chiefly to the 
parablastic group of His and Waldeyer, I propose to return for the present 
to the older name of parablast. I was not enabled to trace the origin of this 
layer in my earlier investigations, and thus failed to grasp its significance. 
More recently I have had an opportunity of studying the development of 
several other types, particularly the herring and cod. In the herring the ger- 
minal mound is not formed until after fertilisation. Partly owing to this cir- 
cumstance, and partly also to the early period at which the assimilation of yolk 
commences, the eggs of the herring are particularly well suited for a study of 
the parablast question. 

In order to understand the relation of the parablast to the yolk and to the 
embryo, it will be necessary to give a detailed account of the structure of the 
ripe unfertilised ovum, and of the early stages of development. In doing so, I 
have compared my results with the earlier investigations of Boeck, Kupffer, 
and Hoffmann. 

The Ripe Unfertilised Ovum. 

The ripe unfertilised ova of the herring vary considerably in size. This varia- 
tion appears to be of a twofold nature. There is a certain variation found in 
the size of ova from a single female, or in those from a particular spawning dis- 
trict. There is also a variation in the average size of ova from one spawning 
district, as compared with those of another. Kupffer (19) found that the ova 
of the Baltic herring have a diameter usually varying between "92 and 1 mm., 

VOL. XXXIII. PART I. 2E 



200 MR GEORGE BROOK ON THE 

while exceptionally small ones may only measure *85 mm. Boeck (2) gives the 
diameter of the herring ova on the Norwegian coast as 1*5 mm. Those which 
I have obtained from the Ballantrae herring averaged 117 mm. in diameter, 
and those of the Loch Fyne herring are about the same size. The egg is 
enclosed in an egg membrane, and outside the latter there is a viscous layer 
by which the ovum adheres to anything with which it comes in contact. It 
is by means of this substance that the eggs become attached to one another 
in the form of flattened cakes. 

Viscous Layer. — If an isolated ovum is gently pressed from a ripe female and 
examined immediately under the microscope, it will be found that the adhesive 
material forms a comparatively even covering around the egg envelope. This 
is even better shown if the egg be pressed out into dilute osmic acid solution, 
or into spirit, and afterwards examined by means of sections. When thus 
hardened the viscous layer usually appears structureless, or presents faint and 
indistinct transverse streaks, such as would be shown in sections of a horny 
substance. Fig. 1 shows a section of the viscous layer and egg membrane in 
the unfertilised ovum. The relative thickness of the viscous layer varies very 
much. When it forms a comparatively even layer around the egg membrane it 
has usually about the same diameter as the membrane itself. When, however, 
before hardening, the viscous substance comes in contact with that of another 
egg, or with a foreign surface, a thickened welt is formed, which may be two 
or three times the thickness of the egg membrane. In such cases there is a 
corresponding thinning out of the layer in other parts of its circumference. 
Although usually structureless, I have once or twice seen well-marked trans- 
verse striations in the hardened viscous layer. Fig. 2 represents such an 
appearance, and is taken from a ripe egg which was pressed directly from 
the oviduct into osmic acid solution. The viscous layer has here about 
the average thickness, but is divided longitudinally into two strata. Each pre- 
sents a well-marked transverse striation, which is more distinct than that in 
the inner portion of the egg membrane. The division of the viscous layer into 
two strata may possibly be due to shrinking, but it appears difficult to see how 
the transverse striations could be brought out by the same cause. They are 
very evenly distributed throughout. 

This structure agrees with Hoffmann's (14) description of the appearance 
of the viscous layer in the unripe egg. According to this author, the zona 
radiata in the nearly ripe egg consists of two layers closely united together. 
The outer layer, which corresponds to the viscous layer, is perforated by very 
fine pore canals, and is sharply separated from the inner portion. In the ripe 
egg, placed directly in l-10th per cent, osmic acid, the pore canals have almost 
entirely disappeared. If the ripe eggs are, however, first brought in contact 
with sea water, and afterwards fixed in osmic acid, the outer layer is seen to 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 201 

be quite separated from the inner one, and to constitute the viscous substance 
which serves for the attachment of the egg. This layer now frequently pre- 
sents a laminated structure. From this description it will be seen that 
Hoffmann regards the viscous layer as a metamorphosed part of the zona 
radiata. In this case it must be regarded as a secretion of the vitellus. 

Egg Membrane. — Kupffer has described two egg membranes, an outer 
zona radiata and an inner one, comparable with the true vitelline membrane of 
other forms. Hoffmann has shown that in their origin these two portions of 
the egg membrane are very similar in structure, and that they are both to be 
regarded as portions of the zona radiata ; there is no true vitelline membrane in 
the herring ovum. My investigations support Hoffmann's conclusions. 

Yolk. — According to Kupffer, the entire contents of the egg envelope are 
divisible into three parts — 

1. A superficial layer, consisting of strongly refractive shining homogeneous 
globules *008 to "02 mm. in diameter, which he terms yolk granules (Dotter- 
korner). 

2. Immediately below the thin superficial layer the yolk consists of larger 
and less refractive yolk spheres, which have a rounded or egg-shaped form. 
They vary in size from "05 to "08 mm., and constitute the greater portion of the 
yolk. These are the Dotterkugeln of Kupffer. 

3. There is also a scanty viscous mass of protoplasm, which is mixed up 
with the other two. 

According to this observer, the fine granular layer of yellowish protoplasm, 
which later forms the blastoderm, is not present in the unfertilised ovum, nor 
is there a germinal disc. 

As Hoffmann has already pointed out, Kupffer was mistaken in supposing 
that the germinal protoplasm does not already exist in the ripe unfertilised 
ovum. The reason why it is not visible in the living egg is twofold. In the 
first place, it does not form a distinct layer around the yolk, as is usually the 
case in Teleostean fish ova; and in the second, there is so slight a difference 
between the colour of the yolk spheres and that of the protoplasm, that in the 
living egg it is impossible to distinguish between them. A section of the unfer- 
tilised egg shows nevertheless that the germinal protoplasm exists in the herring 
as well as in other fish eggs. There is, however, this difference, that whereas in 
fishes generally the bulk of the germinal protoplasm is collected as a distinct 
layer on the surface of the yolk at the time the egg is ready for fertilisation, in 
the herring the protoplasm is distributed throughout the yolk. The egg con- 
tents consist in fact of a mass of delicate protoplasm, in which the yolk spheres 
are imbedded. This structure is well brought out in sections of ova stained in 
Mayer's carmine. I have obtained the best results by leaving the eggs in the 
staining solution from twenty-four to forty-eight hours. Subsequent treatment 



202 MR GEORGE BROOK ON THE 

with acid alcohol extracts all the stain from the yolk, so that the protoplasm 
remains deeply stained with carmine, while the yolk retains its original pale 
yellow tint, which is, however, too weak to show in thin sections. Unless the 
acid alcohol is allowed to act for some hours the yolk is not entirely robbed 
of its stain. 

Fig. 3 (PI. XIII.) represents a section through the middle of an egg, prepared 
as I have described. The germinal protoplasm is seen to be finely granular under 
a high power, but the granulation is so delicate and regular that, with a low 
power, the protoplasm appears quite homogeneous. The large yolk spheres 
occupy the greater portion of the egg, and are comparatively evenly distributed. 
There is not so great a variation in the size of the yolk spheres at this as in 
later stages. Towards the margin, however, there is a diminution in size, 
leading up to the small yolk granules which lie immediately beneath the egg 
envelope. Kupffer says nothing as to the origin of these yolk granules, but 
Hoffmann has indicated their possible mode of origin. According to this 
observer, the unripe ovum contains little protoplasm, and a large number of the 
large yolk spheres about '035 mm. in diameter. It is to be presumed that at 
this stage there are no yolk granules, although this is not distinctly stated. 
Later, in the ripe unfertilised ovum, the large yolk spheres are fewer in number, 
and there is more protoplasm. While most of the yolk spheres are compara- 
tively homogeneous in structure, a few are seen to be filled with smaller spheres 
only '002 mm. in diameter. These are often seen lying in clusters outside the 
larger spheres, and would appear to be set free by the rupture of the walls of 
the latter. Hoffmann does not, however, offer any theory on the subject, nor 
does he give any figures. 

There is undoubtedly a greater proportion of protoplasm to food yolk in the 
ripe ovum of the herring than is to be found at an earlier stage. The small 
refractive yolk granules are also not present in the unripe ovum so far as my 
observations go, but I have not been able to trace their origin. I have never 
observed a collection of small spherical "granules" inside one of the yolk 
spherules, nor any collection of them which would lead one to infer the origin 
assigned to them by Hoffmann. Judging from the subsequent behaviour of 
the food yolk, I am not inclined to accept Hoffmann's view without further 
evidence. The yolk of Teleostean fish ova, and particularly of the herring, is 
simply a collection of food material which has no cellular value whatever, and 
does not undergo a segmentation comparable with that of amphibian ova. If 
Hoffmann's views are accepted, there must either be a segmentation in the 
yolk spheres themselves, or the small yolk granules are the result of a 
mechanical subdivision of the larger masses. The former proposition appears 
entirely unwarranted by the future behaviour of the yolk. A mass of yolk, 
which can form around itself a thin wall, subdivide its contained food material 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 203 

into a number of small spheres, and then by a rupture of its wall set the new- 
products free, must surely possess more vital properties than are exhibited by 
the yolk of fish ova. Again, the appearance of the yolk granules is different 
from that of the yolk spherules. The former are dense and highly refractive, 
while the latter are only slightly refractive. The " yolk granules " disappear 
when the egg is fertilised. They do not appear to be incorporated within 
the protoplasm as so much food, but the dense droplets spread out into a 
thin film, which becomes indistinguishable amongst the germinal protoplasm. 
Such dense droplets are found in the ova of the Gadidse and other fishes, and 
here play a similar part. They are probably oily in nature, and may be pro- 
duced by the mechanical collection of the oily material contained in the yolk 
mass. Returning now to Kupffer's statements concerning the structure of the 
ripe unfertilised ovum, I hold that he is correct in his opinion that the germinal 
disc, in the strict sense of the word, does not yet exist in the unfertilised ovum. 
Undoubtedly he was mistaken in concluding that in the unfertilised ovum there 
is no division into formative and nutritive yolk. This has already been pointed 
out by Hoffmann. This author, however, appears to regard the germinal 
protoplasm, which is distributed throughout the yolk in the ripe unfertilised 
ovum, as homologous with the germinal disc in other fish ova. This is not the 
case. The germinal protoplasm already existing in the unfertilised ovum does 
indeed, after fertilisation, become in great part used up in forming the germinal 
disc, but not entirely so. This protoplasm also increases in bulk considerably 
at the expense of the yolk before segmentation commences. 

Unfortunately, I have not been enabled to make a thorough study of the 
development of the ovarian ovum of the herring. I have, however, examined 
sections of ovaries in various stages of development. The earliest stage which 
I have observed is one in which the primitive ovum is already surrounded by a 
follicle. The cell protoplasm contains very little food material, and the nucleus 
is very distinct. As the ovum increases in size yolk material becomes collected 
within the egg contents to such an extent as to hide the nucleus and its sur- 
rounding protoplasm, when only the whole egg is examined. As development 
goes on it can be made out from sections that the protoplasm increases in bulk 
at the expense of the yolk. It also spreads out amongst the yolk spheres. At 
an early stage the cell protoplasm is star-shaped, having a central somewhat 
thin area in which the nucleus is situated, and around this are a number of 
radiating protoplasmic processes, which are pushed in amongst the continually 
increasing bulk of yolk spheres. In this manner the protoplasm comes to form a 
network supporting the yolk spheres. At a comparatively early stage the ger- 
minal spot becomes obliterated, and the germinal vesicle also loses its primi- 
tively well-marked character. In the ripe unfertilised ovum I have not been able 
to recognise the germinal vesicle. The most approved methods of staining do 



204 MR GEORGE BROOK ON THE 

not bring out any differentiation in the germinal protoplasm. The latest phase of 
the germinal vesicle which I have observed is represented in fig. 4. 

It is here somewhat quadrangular, but irregular in outline, and from its 
margin fine threads of protoplasm are seen to penetrate the yolk mass. With a 
magnifying power of 700 diameters a beautiful reticular arrangement of the 
fibrillar can be made out. There are distinct thickenings at the nodes, and 
besides the fibrillar reticulum there are a very large number of very small 
granules, which stain deeply with carmine. I have not been able to make 
out the process of degeneration which the germinal vesicle probably under- 
goes prior to the ovum becoming mature and ready for fertilisation. 

The difference then between the ripe ovum of the herring and that of other 
Teleostean fishes appears to rest in the fact, that at the time the herring ovum is 
ready for impregnation the germinal protoplasm is not collected into a definite 
layer. - Changes in the arrangement of the egg contents therefore occur in the 
herring ovum after fertilisation, which in the majority of fish ova have already 
been brought about without the aid of spermatozoa. 

Kupffer also maintains that the relationship of the various parts of the ripe 
unfertilised ovum remains unaltered in sea water, so long as the egg remains 
unfertilised; in other words, that sea water, per se, has no influence on the 
ovum. On this point Boeck and others are at variance with Kupffer. The 
experiments which I have already described* were in part devised to test this 
point, and all tend to show that Kupffer's conclusion was justified. Others 
which were conducted more recently only tend to strengthen the same view. 
In the first place, the egg membrane does not separate from the yolk unless it 
has previously been penetrated by spermatozoa. Whether these enter at the 
micropyle only, or may force their way through the egg envelope at any part, 
I have not been able to decide; but the fact remains that unless an egg is sub- 
mitted to the action of spermatozoa, the egg membrane does not separate to 
any appreciable degree from the yolk. In this connection reference may be 
made to my experimental researches of the fertilisation of herring ova (7). 
In one experiment, eggs which had remained unchanged for tiventy-four hours in 
sea water were submitted to the action of spermatozoa. Within an hour the egg 
membrane had separated to a considerable extent from the yolk in a large 
number of the eggs. Although in most cases the eggs at this time retained only 
a feeble vitality, and the viscous covering of the egg membrane had become so 
hardened as to offer considerable obstruction to the entrance of spermatozoa, 
a breathing chamber was formed in the normal manner. It is evident, then, 
that the entrance of spermatozoa is necessary before this separation can take 
place. If the micropyle is an open canal, communicating freely with the 
surface of the yolk, there appears no reason why water should not enter the 

* Annual Keport of the Fishery Board for Scotland, 1885. 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 205 

egg through this channel. It would seem, however, on a priori grounds, that 
a micropyle can be of little service in aiding fertilisation in such an egg as that 
of the herring. Around the egg envelope at the time the egg leaves the ovi- 
duct there is a comparatively thick layer of a viscous substance which hardens 
in sea water. So long as it remains semifluid it collects at the lower pole, and 
if two or more eggs are in contact, the viscous substance around each forms a 
thick ring around the point of contact, and thus the whole mass is cemented 
together. It follows, therefore, that the moment an egg touches any object in 
its descent through the water it becomes attached to that object, and does not 
again change its position during development. It seems probable that the 
micropyle cannot have a fixed position in relation to the axis of the ovum, as 
is the case in pelagic ova. If this supposition is justified, it follows that the 
micropyle must frequently be covered by the thicker portions of the hardened 
viscous layer. In any case the opening of the micropyle must be filled with 
the viscous layer before this hardens, as Kupffer has already pointed out. 
Thus spermatozoa would find as much difficulty in penetrating the ovum at the 
micropyle as at any other point. It has been proved by repeated experiment 
that herring ova may be fertilised from twelve to twenty-four hours after they 
have been placed in sea water, and by this time the viscous layer is so hard that 
the ova are not easily displaced from their point of attachment. In any case, 
therefore, spermatozoa are able to penetrate this hardened layer, which indeed 
offers more resistance than the egg membrane itself. It has been generally 
admitted that in fish ova the spermatozoa enter by the micropyle and by this 
only. The presence of a viscous covering of the egg envelope in such ova as 
that of the herring may modify the use of the micropyle. If the viscous 
covering of the eggs of the herring and allied forms is phylogenetically of recent 
origin, it may be that the changed conditions have rendered the micropyle 
useless. These remarks are, however, simply offered as suggestions, a 
thorough investigation of the whole subject being very desirable. 

The behaviour of the germinal protoplasm during the time that a ripe 
unfertilised ovum remains in sea water cannot easily be observed in the living 
egg. In order to investigate this point, I have cut sections of a large number 
of eggs which have remained unfertilised in sea water for a time varying from 
one to forty-eight hours, and I have also examined sections of ripe ova taken 
from females which had been dead some hours. As I have previously described, 
the germinal protoplasm at first forms a comparatively even network between 
the yolk spheres. There is, it is true, a little more protoplasm at the surface of 
the yolk than towards the centre, but it must be remembered that the yolk 
spheres are smaller towards the surface, and there is thus more room for the 
protoplasm. This exact relationship is not long maintained in any case. There 
is, however, a difference in its behaviour in the fertilised and in the unfertilised 



206 MR GEORGE BROOK ON THE 

ovum. The immediate effect of fertilisation is that a true germinal disc is 
formed, of which the protoplasm already existing in the ripe unfertilised ovum 
forms only a part. Such changes never take place without the stimulating aid 
of spermatozoa. Their exact nature will be described in due course ; for the 
present it will be sufficient to describe the behaviour of the germinal proto- 
plasm in the unfertilised egg. Simply stated, the germinal protoplasm acts 
as so much passive material so long as the egg remains unfertilised. It collects 
very slowly to the surface, it is true, but in a very different manner to that in 
which it would if fertilised. There is a gradual accumulation at the surface, 
and day by day the protoplasmic network is withdrawn more and more from 
the centre, but it never collects into a disc-like prominence in the unfertilised 
ovum. After a week's immersion in sea water an unfertilised ovum presents 
the appearance shown in fig. 5. It only differs from the recently-matured 
ovum in having more protoplasm around the circumference and less towards 
the centre of the egg. The protoplasmic filaments are never withdrawn to 
nearly the same extent in the unfertilised as in the fertilised egg. In the 
fertilised egg there are a number of branching protoplasmic filaments connecting 
the germinal disc with the yolk, but in the yolk pole the protoplasm is almost 
entirely withdrawn. In the unfertilised egg which has been some days in sea 
water this is not the case. The protoplasm forms a comparatively even layer at 
the surface of the yolk, and there is no division into animal and vegetative poles, 
the protoplasmic filaments not being withdrawn more at one part than at another. 
It should be pointed out that this partial collection of the germinal protoplasm 
at the surface will take place ivJiether the egg is placed in sea water or not. In 
order to conduct the experiment already referred to, ripe females were kept for 
a varying time in moist cloths. Sections of eggs kept under such conditions 
show that the germinal protoplasm begins to collect at the surface of the yolk 
soon after the egg is ripe, and that the amount of protoplasm found at the 
surface is, roughly speaking, proportional to the time which has been allowed 
to elapse before examination. Thus, then, sea water has nothing to do with 
causing the protoplasm to collect at the surface, nor, so far as I could make 
out, is this accomplished more rapidly in sea water than in the ovary itself. 

Formation of the Germinal Mound. 

The fact that at the time of impregnation the ovum of the herring exhibits 
nothing of the nature of a germinal disc, in the ordinary sense of the word, is a 
point of very great interest. In the history of the majority of fish ova, the 
influence of the sperm is not necessary for a separation of the germinal disc 
from the yolk, as this separation has already taken place before fertilisation. 
The case of the herring is, therefore, specially interesting from the fact that this 
accumulation of the germinal protoplasm at one pole can be watched under the 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 207 

microscope in the living egg. Kupffer has made an elaborate series of inves- 
tigations on the formation of the blastoderm in the herring ovum. He con- 
cludes that the germinal disc is formed by the combined influence of sea water 
and spermatozoa. Kupffer's conclusion is undoubtedly true to a certain 
extent, though not exactly in the manner in which he intended it. He was of 
opinion that the act of fertilisation brought about changes in the egg contents 
which resulted in the separation of the germinal protoplasm from the yolk, and 
the collection of this into a definite mound at the animal pole of the ovum. 
Although he mentions a certain small quantity of protoplasm mixed amongst 
the yolk spheres, he does not appear to have been aware that there is in the 
ripe unfertilised herring ovum a considerable collection of germinal protoplasm 
distributed throughout the yolk, the greater portion of which ultimately forms 
the germinal disc. Nevertheless, he was correct in the sense that the germinal 
protoplasm is not collected into the form of a disc until after fertilisation. On 
this account it appears to me that Hoffmann is not entirely justified in his 
assertion that in the herring, as in other Teleostean fishes, the germinal layer 
exists before fertilisation. As we have seen, the germinal protoplasm which 
exists in the unfertilised egg must undergo a further development and growth 
before a germinal layer exists, which can be compared with that existing in 
most Teleostean fish ova before fertilisation. Van Bambeke (3) has called 
attention to the same point, and has shown that in Tinea vulgaris, as well as in 
the herring, the influence of spermatozoa is necessary before a true germinal 
disc is formed. If the germinal protoplasm existing in the unfertilised ovum 
simply collected at the surface after fertilisation, and then commenced to seg- 
ment, it would be another matter. This protoplasm would then be directly 
comparable with the germinal disc or germinal layer of other fishes. If by the 
germinal layer is understood an amount of protoplasm which is distributed 
throughout the yolk, which, as a result of fertilisation, collects at the surface, 
grows at the expense of the yolk, and after a considerable increase in its bulk 
begins to segment, then there is a germinal layer in the ripe unfertilised ovum 
of the herring. But surely technical terms should have a definite and limited 
meaning, and it is impossible to regard the germinal layer of such eggs, for 
instance, as those of the Gadidce, as equivalent with the protoplasm which, in 
the ripe unfertilised ovum of the herring, is distributed throughout the nutritive 
yolk. 

Let us glance for a moment at the structure of a pelagic Teleostean ovum. 
The yolk is very transparent, and is not divided into a large number of yolk 
spheres, but consists only of one large vitelline sphere, which is comparatively 
homogeneous in structure. There may or may not be a special condensation of 
the oily contents into definite oil globules. From the fact that the yolk con- 
sists only of one large yolk sphere the outline is smooth, and there are no 

VOL. XXXIII. PART I. 2 F 



208 



MR GEORGE BROOK ON THE 



indentations of the surface of the vitelline mass as in the herring ovum. Out- 
side the yolk the germinal protoplasm is collected into a distinct layer, usually 
of a pale yellow tint. This layer is always sharply marked off from the yolk 
at the time the ovum leaves the oviduct. As the egg floats in the water the 
germinal layer collects at the lower pole, leaving only a delicate film of proto- 
plasm around the upper portion of the yolk sphere. Segmentation then 
commences if the egg has been fertilised. In the herring, however, the changes 
are somewhat different. At a period varying from fifteen to thirty minutes 
after the introduction of spermatozoa to sea water containing ripe eggs, the egg 
membrane begins to leave the yolk, and by the time an hour has elapsed the 
membrane has expanded to such an extent that a large cavity is formed all 
around the vitelline mass. This cavity is filled with water, which probably 
contains a portion of the egg contents in solution. The accompanying table 
shows the increase in the size of the egg after inception of water. The first 
two items are the measurements given by Kupffer, and may be taken as a 
type of the eggs of the Baltic herring. The others are measurements of the 
eggs of herring taken from the Ballantrae Banks, off the Ayrshire coast. 



Diameter 

of 

unfertilised 

oito' 

of*" 



•92 mm. 
1 - mm. 

1-194 mm. 



average 
1-1759 mm. 



Diameter 
of yolk 

after 
1 hour. 



1-147 mm. 



Diameter of 

egg capsule 

after 

1 hour. 



T486 mm. 



Diameter when breathing chamber is complete. 



Yolk. 



Greatest 
diameter. 



•85 mm. 
•97 mm. 

1-298 mm. 



Diameter 
at right 
angles. 



•82 mm. 
•92 mm. 

1-204 mm. 



Egg capsule. 



Greatest 
diameter. 



1"2 mm. 

1-29 mm. 

1-768 mm. 
(after 5 hours) 
1-599 mm. 
1-599 mm. 
1-599 mm. 
1-542 mm. 



Diameter at 
right angles. 



(after 45 rnin.) 



) 

165 mm. 
(after 5 hrs.) 
1-580 mm. 
1-486 mm. 
1-448 mm. 
1-430 mm. 



The eggs with which Kupffer experimented were smaller than those from 
Ballantrae, but even taking this into account, it will be seen that the latter 
have proportionately a considerably greater diameter after the breathing chamber 
is formed. Kupffer's measurements were made forty-five minutes after fer- 
tilisation, and he does not state whether any further increase in the diameter 
of the egg capsule was noticed at a later period. In the measurements which are 
given for comparison, it will be seen that in example No. 3 the egg capsule 
measured 1*486 mm. one hour after fertilisation. At this stage both yolk and 
egg capsule were comparatively globular. At this stage the germinal proto- 
plasm had collected to a considerable extent to the surface of the yolk, but was 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 209 

fairly evenly distributed around it. The later measurements are taken at a 
stage when the germinal protoplasm has collected into the form of a mound at 
the animal pole of the ovum. The greatest diameter therefore passes through the 
axis of the ovum at this stage. Whether the measurement 129 mm. represents 
the largest diameter which is reached by the eggs of the Baltic herring I cannot 
say, but it is probable that if there had been any further increase Kupffer 
would have noted it. The early period at which this diameter was reached is 
probably to be attributed to the temperature at which the experiments were 
conducted. The temperature of the water during my experiments at the 
Rothesay Aquarium varied between 40° and 42° F. ; whereas it is probable the 
temperature was considerably over 55° F. during Kupffer's experiments, as 
his embryos hatched out on the seventh clay. Dr Meyer (22) has shown that 
young herring hatch out on the tenth or eleventh clay at a temperature between 
51°*8 and 53°6 F. ; whereas at 32° F. the earliest embryos do not hatch until 
the forty-seventh day. As the egg membrane leaves the yolk the surface of 
the latter can be more easily studied. It is then seen that the " yolk granules " 
on the surface are rapidly disappearing. Kupffer says they are dissolved. 
However this may be, neighbouring "yolk granules" may be seen to run 
together and flatten out into a thin pellicle, which soon becomes indistin- 
guishable, with the large yolk spheres for a background. They behave, in fact, 
very much like the small droplets of an oily nature which are found on the 
surface of the egg of the cod before fertilisation. Whether the " yolk granules " 
are really oil globules, or only yolk material richer in oil than the larger spheres, 
I cannot say, but their behaviour would seem to support the former supposi- 
tion. Kupffer next describes a series of clear vacuoles which arise at the 
surface of the yolk as transparent spots. These increase rapidly in size, and 
are pushed forward towards the centre of the yolk as a network of fine tubes. 
With the appearance of the clear vacuoles the germinal protoplasm begins to 
collect on the surface of the yolk. I have never been able to observe the 
vacuoles which Kupffer describes, although I have searched for them 
repeatedly. With the act of fertilisation an activity is set up in the germinal 
protoplasm which causes it to collect rapidly on the surface of the yolk. Very 
early in this process the outer yolk spheres are a little wider apart than those 
towards the centre, and the protoplasm as it collects fills up the spaces between 
them. A little later the protoplasm is almost entirely withdrawn from the 
centre of the yolk, and there is then a thin layer of protoplasm on the surface, 
with a number of branching root-like processes extending some distance into 
the yolk. It is, I think, this collecting protoplasm which Kupffer has 
mistaken for vacuoles and his series of coarse tubes. In sections of the egg 
about this stage which have been mounted unstained the germinal protoplasm 
is very transparent, whereas the yolk spheres are quite granular and of a 



210 MR GEORGE BROOK ON THE 

yellowish tint. The appearance in the living egg is thus explained. The 
transparent portions between the yolk spheres are not vacuoles, and a system 
of tubes pushed down into the yolk, but the channels by which the germinal 
protoplasm (of which Kupffer had no cognisance) makes its way to the 
surface. An hour after fertilisation (at 41° F.) a considerable quantity of the 
germinal protoplasm has collected at the surface of the yolk, and forms a 
distinct layer, varying from '0188 to "0564 mm. in thickness. At first this is 
quite clear and homogeneous, but soon fine granules make their appearance, 
and the whole layer becomes darker in tone. 

From the moment that a layer of protoplasm has collected at the surface, 
an interesting series of phenomena is commenced, which is only terminated 
when the whole of the nutritive yolk has been consumed. The germinal pro- 
toplasm begins to grow at the expense of the yolk. Large masses of yolk are 
incorporated within the substance of the protoplasm and digested there. 
During this time the protoplasm is in constant motion, and flows slowly in 
thicker and thinner waves around the yolk. These phenomena are not new, but 
form part of a process which has frequently been described in connection with 
the parablast. They are, however, more marked and easily followed in the 
herring than in any other form with which I am acquainted. The process is 
one of intracellular digestion, and at a later stage probably forms an important 
mode in which the food yolk is used up in most meroblastic ova. The im- 
portant point to be noted for the present is, that in the herring the yolk is 
partly consumed to form the germinal disc itself. Kupffer supposed that 
nearly the whole of the germinal disc was formed in this manner, but it is 
probable that he had not studied sections of the egg in the earliest stages of 
development. He says, to begin with, that the formative yolk appears as a 
continuous superficial layer. It has already been seen that this is not so. 
When the greater portion of the germinal protoplasm has collected at the 
surface of the yolk, the appearance in an optical section of the living egg is no 
doubt as Kupffer describes. Optical sections are, however, very misleading, 
and should only be used in helping to explain the appearance shown in actual 
section. A little experience may teach one how to interpret optical sections, 
but this experience can only be obtained from a study of actual sections of 
the egg. 

Fig. 6 represents an optical section of the living egg of the herring an 
hour after fecundation. The germinal protoplasm is seen as a continuous 
superficial layer, which is considerably thicker at one side. The protoplasm is 
filled with fine and larger granules, and a number of small clear vesicles may 
also be made out under a moderately high power. The superficial layer of 
"yolk granules " has entirely disappeared, and the yolk now consists of a mass 
of large yolk spheres, which appear to be evenly distributed throughout. A 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 211 

careful examination of the peripheral row of yolk spheres shows that as yet 
there is little irregularity in their size and position. So much for the appear- 
ances presented by an optical section; let us now turn our attention to a 
stained section of the same stage. Such a section is represented in fig. 7. 
Remembering the structure of the ripe unfertilised ovum, it is easy to see now 
that the germinal disc is in process of formation. The protoplasm in collecting 
towards the surface has followed certain channels between the yolk spheres. 
There is still, however, a considerable portion of the protoplasm mixed amongst 
the yolk in the form of branching processes communicating with the surface 
layer. These processes vary in thickness, and also in their number and distri- 
bution in different parts of the circumference. Towards the germinal pole they 
are stronger, and penetrate further into the yolk than at any other point. In 
the yolk pole the filaments rarely penetrate beyond the second row of yolk 
spheres. The protoplasm is seen to be highly granular, and also to contain a 
number of small masses of yolk. It will thus be seen that the true relation of 
protoplasm to food yolk cannot be made out in optical section. 

The appearance of granules in the protoplasm is the first sign of an active 
vegetative period in the history of the germinal protoplasm. In the section 
under consideration the digestive process has only just commenced, so that it 
may be better studied at a little later stage. Fig. 8 represents a section of an 
egg five hours after fertilisation, and at a time when the germinal protoplasm 
has almost entirely collected towards the germinal pole. Large masses of yolk 
are seen to be entangled in the protoplasmic processes, and throughout the 
germinal disc itself there are a number of yolk masses varying in size. At this 
stage great activity is manifested by the protoplasm immediately adjoining the 
yolk, and, as already stated, the whole mass of the germinal protoplasm has an 
undulating movement. In the living egg it frequently happens that there is a 
large temporary collection of the germinal protoplasm at the yolk pole. This 
has been termed the Gegenhugel by Kupffer. Sometimes this accumulation 
is so large that it may easily be mistaken for the true germinal area. 

At this stage Kupffer describes an appearance in the living egg, which is 
intimately connected with the growth of the germinal disc. He says that 
when the germinal protoplasm forms a distinct layer on the surface of the yolk, 
the surface vacuoles disappear, and there remains only one or a pair of large 
lacunw in the centre, which are often continued towards the flat base of the 
germinal disc by a stalk. These have much in common with the latebra of 
the hen's egg. According to Kupffer, these lacunae are not to be considered 
as distinct caverns, but as transition areas (Schmelzung sheer de) in which the 
globular yolk masses are transformed into a more clear and uniform mass. 
These, he maintains, are to be found till the end of development. Ryder sug- 
gests that the lacunas, as described by Kupffer, do not normally exist, but that 



212 MR GEORGE BROOK ON THE 

they are produced by the hardening reagents used in preserving the ova. Such, 
however, is not the explanation. It is in the living egg that such an appear- 
ance is seen (see fig. 9) before any reagents have been used. There are no 
such lacunae to be found in sections of hardened material. The appearance, I 
think, admits of a similar explanation to that which has been given for the 
"vacuoles," of which it is supposed to be the remnant. The base of the ger- 
minal disc is not flat, as was supposed by Kupffer. There are proceeding 
from it a number of broad but tapering strands of protoplasm, which form the 
means of communication between the germinal disc and the yolk. In this 
region the mixture of yolk and protoplasm is more transparent than the more 
solid yolk mass, and thus in optical section appears as a cavity. The peculiar 
shape of these so-called lacunae appears to be altered by hardening agents, as 
I have never in section met with such flask-shaped masses as are seen in 
the living egg. Later, as the protoplasmic filaments are withdrawn, the central 
mass of yolk spheres lose their rounded outline, and appear to fuse together; 
whereas the more peripheral ones retain their primitive form, being always 
more or less surrounded with protoplasm. Thus, again, in these later stages 
the central portion appears more transparent than the peripheral zone. 
Kupffer's interpretation also requires modification in another respect. One 
is led to conclude from his remarks that the yolk is directly transformed into 
protoplasm in the " transition area " already spoken of. This is not really the 
case. The yolk only becomes available for the use of the blastoderm after it 
has been assimilated and digested by the existing protoplasm. While the 
germinal disc is in progress of formation, its somewhat conical and ill-defined 
base is actively engaged in this process of assimilation. In the base of the 
disc large masses of food yolk may be seen entangled between the branching 
filaments, and these get smaller and smaller as they are pushed farther away 
from the active area. 

It is important to note that at the time the upper portion of the disc is 
ready for segmentation the lower portion is still actively fulfilling a vegetative 
function. 

It thus comes about that both Kupffer and Hoffmann were partly correct 
in their conceptions of the germinal disc, but, according to my view, neither of 
them were entirely so. It is by a union of both ideas that a true compre- 
hension of the question is obtained. 

The egg of the herring has now reached a stage when it is comparable with 
those of other fishes. Indeed, so nearly does it approach to Waldeyer's (26) 
ideal of a meroblastic ovum that it might very well have served as his type. 
Before the first furrow appears the egg is made up as follows : — 

1. Of a large collection of protoplasm in the germinal area in which segmen- 
tation subsequently commences. 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 213 

2. Of a thin film of cortical protoplasm entirely surrounding the yolk, and 

which frequently presents a considerable dilatation at the yolk pole. 

3. Of a number of filamentous protoplasmic processes, mainly confined to 

the base of the germinal area, which serve to keep up a communication 
between the latter and the more purely nutritive yolk. 

4. Of the nutritive yolk itself, which constitutes the greater portion of the 

ovum. 

Thus it will be seen that the egg of the herring fulfils all the conditions of 
Waldeyer's typical meroblastic ovum. The r61e played by these constituent 
parts in the economy of the embryo is very marked. The part played by the 
cortical protoplasm, and the root-like filaments, is particularly well brought out 
in the herring. A discussion of the whole subject will, however, be deferred 
until we consider the origin and growth of the parablast. Shortly before the 
appearance of the first furrow the disc as seen in optical section has a diameter 
of "84 mm., and is *28 mm. in thickness. On account of the collection of the 
germinal protoplasm at one pole the egg loses its previously rounded outline, 
and has now a diameter of 1*60 mm. in its longer axis, and 1*48 mm. in a 
direction at right angles to this. 

Segmentation. 

The appearance and behaviour of the first segmentation nucleus in the fish 
ovum has not been satisfactorily explained. Hoffmann (14), indeed, has 
figured in a very diagrammatic manner the appearance and position of this 
nucleus when it first divides; but so far as I am aware his observations have 
not been confirmed, nor have they received any support from the work of recent 
investigators. In the case of the herring I have used the most approved 
methods of fixing and staining the material, but have as yet failed to observe a 
nucleus of any kind until after the third furrow has been formed. The gradual 
disappearance of the germinal vesicle in the ovum as it approaches maturity 
has been already alluded to. Judging from analogy, a portion of the germinal 
vesicle must remain as the female pronucleus. Having failed to demonstrate 
this as a defined and recognisable mass, it appears necessary to assume that it 
is distributed throughout the germinal protoplasm. I am not prepared to prove 
this view, which undoubtedly is not in harmony with our information in other 
cases, but it receives considerable support from a knowledge of the behaviour of 
the germinal protoplasm during the early segmentation stages. At the time of 
the appearance of the first furrow I have not succeeded in demonstrating a 
nucleus either in the living egg or in prepared material. It has thus been 
impossible to test the statements of Kupffer and Hoffmann as to the direc- 
tion of the first plane of cleavage from actual observations of the nucleus, or of 



214 MR GEORGE BROOK ON THE 

any trace of karyoldnctic figure. So far as the herring is concerned, other 
phases of the process may be followed, which give a clue not only to the 
direction of the early planes of cleavage, but also show in a most decided 
manner the true nature and mode of origin of the two primary germinal areas 
— the archiblast and parablast. 

According to Kupffer, the first furrow is meridianal in direction — that is, 
in the direction of the axis of the egg. The second is equatorial, and with the 
completion of this the germinal area is divided into archiblast and parablast. 
The third furrow is meridianal, but at right angles to the first, and after this 
the segmentation proceeds in the usual way. 

Hoffmann, on the other hand, maintains that in the fish ovum the first 
segmentation furrow takes an equatorial direction, so that instead of the first 
cleavage process resulting in the formation of two segmentation spheres, the 
germinal area is divided into two layers corresponding to the archiblast and 
parablast, each of which contains half of the original segmentation nucleus. 
According to this arrangement, the parablast is given an equal value with the 
archiblast at the outset, and yet Hoffmann denies that it takes any part in the 
formation of the tissues of the embryo. 

The majority of observers have not described an equatorial furrow in the 
Teleostean fish ovum until a considerably later stage, and it has been generally 
accepted that there is no furrow in the fish ovum which is equivalent to the 
first equatorial furrow (the third of the series) in the amphibian ovum. 

Agassiz and Whitman (1) differ from other investigators in attributing the 
whole of the germinal protoplasm in the first instance to the archiblast, and 
derive the nuclei of the parablast from the archiblast as secondary products 
which are derived from its marginal cells. 

From my own investigations, I conclude that in the herring, as in so many 
other forms, the first furrow which takes an equatorial direction is the third 
of the series. This furrow is therefore comparable with the third furrow in the 
amphibian ovum. 

After the protoplasm in the germinal area has increased considerably in 
bulk at the expense of the yolk, there is usually a comparatively quiescent 
period. During this stage a part of the germinal protoplasm collects at the 
yolk pole, and there forms a small mound. As soon, however, as the first traces 
of a furrow are to be seen this mound gradually disappears, and the protoplasm 
of which it was formed slowly travels along the surface of the yolk to join in 
the approaching period of activity in the germinal area. There remains, how- 
ever, a thin film of protoplasm around the yolk both in this and in later stages. 
This does not form a flat layer, but is seen in section to follow the outline of 
the yolk spheres, and frequently to fill in the spaces between them. 

The surface of the germinal protoplasm, which has hitherto been much 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 215 

arched, commences to flatten towards the centre. As a result of this flattening, 
a vertical furrow is slowly pushed down towards the surface of the yolk, as 
seen in optical section, but stops short some distance above the latter. A study 
of stained sections of this stage shows several points which cannot be made 
out in the living egg. The upper portion of the germinal area contains very 
little food yolk, but between this and the main body of the yolk material there 
is a somewhat triangular area containing a larger quantity of yolk imbedded in 
the protoplasm, and from the base of which the protoplasmic processes are 
pushed down into the yolk. This area is actively engaged in assimilating food 
material, and is crowded with particles of yolk. At the time, therefore, that 
the upper and older portion of the germinal area is ready for segmentation, the 
material included in the lower portion adjoining the yolk is not so far advanced. 
It is one of the recognised laws of segmentation that the rapidity with which 
any part of an ovum segments varies, ceteris 'paribus, with the relative amount 
of protoplasm it contains. The protoplasm in this vegetative portion of the 
germinal area contains as yet too much undigested yolk for it to take part in 
the segmentation process. Thus the first furrow progresses more slowly as it 
approaches this area, and for the time being is arrested before it has reached 
the base of the germinal disc. Another point is also shown in sections of this 
stage, which will be considered more fully at a later period, but which should 
be mentioned here. The first furrow is not a continuous plane of cleavage in 
the first instance. There are in the line of cleavage a series of small vacuoles, 
which, as they become more elongated, run together, and so form a considerable 
portion of the furrow. Thus the first two segmentation spheres are in part 
separated by a process of vacuolation. The first two segmentation spheres 
become entirely separated from one another at their upper poles, the series of 
vacuoles aiding considerably in this process. The germinal area is thus divided 
into two portions, which are completely separated above, but which are united 
at the base, the first furrow not having completely penetrated to the base. 

After the first furrow has been formed, a comparatively quiescent stage 
follows, during which a part of the germinal protoplasm again collects in a 
mound at the yolk pole. This is not an accidental occurrence, but has been 
already observed by Kupffer, and I have had frequent opportunities of 
observing this process. During this quiescent period it is usual for a nucleus 
to make its appearance towards the centre of each segmentation sphere in 
pelagic fish ova. Such nuclei in the living ovum have the appearance of a 
more transparent area, usually distinctly marked off from the surrounding 
protoplasm. They usually disappear again before the next active stage begins, 
again to reappear during the following quiescent period. I have not observed 
such nuclei in the living egg of the herring at this stage, nor have I been 
able to make them out in stained preparations. 

VOL. XXXIII. PART I. 2 G 



216 MR GEORGE BROOK ON THE 

The formation of the second meridianal furrow is merely a repetition of 
what has been described for the first. The protoplasm at the yolk pole again 
joins that in the germinal area, and a second furrow is formed at right angles 
to the first. This second furrow, like the first, does not quite reach the base 
of the germinal protoplasm. When the first two furrows are completed, the 
protoplasm in the germinal area is imperfectly divided into four segments, 
which are not denned at the base. There is again a quiescent stage during 
which a small thickening of germinal protoplasm is again to be seen at the 
yolk pole. 

The next furrow is equatorial in direction, and simply completes the 
contour of the four existing segmentation spheres. Before this can be formed, 
the protoplasm through which it will pass must have so far completed its 
process of assimilation as to allow segmentation to proceed. Shortly before 
the equatorial furrow commences, the protoplasm at the yolk pole again joins 
that in the germinal area, and the furrow is then formed very slowly, and 
is at first indistinct. It is situated towards the base of the germinal area, 
and with its completion there are formed four segmentation spheres, which 
are now isolated from the yolk. Below the furrow a small portion of the 
germinal protoplasm remains, part of which forms branching processes into the 
yolk immediately below the segmented portion, and the remainder becomes 
distributed around the yolk mass. 

There is thus set up a division into two distinct layers, the archiblast and 
parablast. The archiblast is cut off from further direct communication with the 
yolk, and goes on segmenting. The parablast comprises that portion of the 
germinal protoplasm which is not included in the archiblast, and which 
remains as a connecting area between the latter and the yolk. For the time 
being it remains comparatively inactive, but later has a very important part 
to play. 

The time occupied by all these changes is about 9^ hours, at a temperature 
of 41° to 44° F. There is a slight variation in the rapidity with which the 
various eggs develop, which becomes more marked as development proceeds. 
The following table shows the details of the process : — 

Commencement of 1st furrow, 6| hours after impregnation. 
Completion „ 6f hours 

Commencement of 2nd furrow, 7| hours 
Completion „ 8J hours 

Commencement of 3rd furrow, 9 J hours 
Completion „ 9f hours 

It will be noticed that in each case there is an hour's interval between the 
completion of one furrow and the commencement of the next. According to 
Kupffer's observations, the first furrow commences about two hours after 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 217 

impregnation. He does not, however, state the temperature at which the 
observations were made, but I gather from remarks in another portion of the 
paper that this was probably between 60° -8 and 64° 4 F. 

The influence of temperature on the rate of development of fish ova is 
very great, and has been already studied by Meyer in the case of the herring. 
The sensibility of the ova of the herring to a change of temperature is almost 
as marked as that of pelagic fish ova. There can be no doubt, however, that 
under natural conditions the eggs of the herring are not so liable to sudden 
changes of temperature as are those which float at or near the surface of the 
sea. The range of temperature at which the eggs of the herring will develop 
normally is much wider than is the case for the eggs of the Salmonidse. 

On the completion of the four-cell stage — that is, after the formation of the 
third furrow — the segmented disc measured in one case 9407 mm. in diameter, 
and *3198 mm. in thickness ; in another egg the measurements were *9595 
mm. and "2822 mm. respectively. After the furrows are completed, the 
individual cells separate more or less from one another. This is accomplished 
in the following manner : — The adjacent cells begin to separate at the outer 
limit of the furrow between them, and at the same time a similar process 
commences at the inner extremity of the same furrow. Thus, at the point 
where the two furrows cross one another, there is a space formed, owing to 
the protoplasm receding somewhat from the former point of contact. In this 
respect the segmenting disc of the herring ovum presents a very different 
appearance from that which is seen in many other fish ova, for instance those 
of the Salmonidae. Such an arrangement is of frequent occurrence amongst 
the Invertebrata, and is there connected with the formation of the segmenta- 
tion cavity. In the herring the segmentation cavity arises at a much later 
stage, and has no connection with this structure, which, indeed, is here 
only a temporary one. As the cells become more completely separated, the 
central cavity is lost. This mode of separation of the cells in the early 
segmentation stages is not confined to the herring amongst fishes. A similar 
phase is found in the ova of Perca, Leuciscus, and other forms. In the species 
which show this partial separation of the early segmentation spheres, the 
cells at a later stage are always loosely aggregated together. On the other 
hand, in the group of which Salmo may be taken as the type, the cells are 
never so completely separated from one another, and there is almost an 
entire absence of those large spaces between the cells during the segmentation 
stage, which are of such common occurrence in the herring ovum. In this 
respect Salmo approaches more nearly to the Elasmobranch type, and the 
difference is probably connected with the distribution of food yolk. 

Under normal conditions the separation of the four cells is never complete 
in the herring ovum. They present the appearance of four conical mounds 



218 MR GEORGE BROOK ON THE 

united towards the base. I have seen similar effects in the eggs of the 
Gad'uhv, but these, I think, have been caused by too great an elevation of 
temperature. In such cases the separation may become complete, when develop- 
ment is at once arrested, and the egg dies. 

Returning now to the position held by Kupffer, it will, I think, be seen 
that he must have been mistaken in the order of segmentation. It is only 
fair to state that his opinion, that the second furrow takes an equatorial 
direction, was founded on an observation of the process in the pike, and not 
in the herring. He concludes, however, that the early phases of segmentation 
are identical in both species. If the second furrow is equatorial in direction, 
why should the cortical protoplasm flow forwards from the yolk pole to the 
germinal area when the third furroiv is about to be formed ? If there is an 
equatorial furrow already in existence, the upper portion of the germinal 
area which it defines must be cut off from communication with the lower 
part, and with the yolk. That this is not the case is shown by the fact 
that after the formation of each of the first three furrows, the cortical proto- 
plasm diminishes in quantity. There is a further point. The cortical proto- 
plasm flows from the yolk pole to the germinal area, and becomes a part of 
the latter during each of the first three segmentation stages. After this the 
remaining cortical protoplasm, which has very much decreased in bulk, does 
not again flow towards the germinal disc, until the latter consists of a mulberry 
mass of cells, and awaits the co-operation of the parablast. The cortical 
protoplasm continues to exist, and indeed to increase in bulk, but it is 
evident it can no longer take part in the segmentation of that portion of 
the germinal area which has been cut off from communication with it by 
the formation of an equatorial furrow. Nevertheless, it has a very important 
part to play. 

The same arguments may be brought against the assertion of Hoffmann, 
that the first furrow takes an equatorial direction in the fish ovum. Hoffmann 
appears very certain about his interpretation, and gives a figure in which the 
nucleus is situated towards the base of the germinal disc, and in which the 
elongation of the nucleus during karyokinetic division takes a vertical direction. 
The plane of division is therefore at right angles to the nuclear axis, so 
that an equatorial furrow is formed. 

It would not be just to deny the accuracy of such observations from a 
study of different material. Hoffmann's investigations were made on Julis, &c, 
and mine on the herring. It is possible that a difference in species may 
allow of a difference in the order of development. All I can say is, that 
in the herring neither the first nor the second furrow takes an equatorial 
direction, according to my own interpretation of the process. If either of them 
did, the whole plan of development would, to my mind, be changed. 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTBI. 219 

Having concluded that the third furrow takes an equatorial direction in 
the herring ovum, it will be well to reflect on the significance of this fact. The 
main portion of the germinal protoplasm, which constitutes the archiblast, 
forms the animal pole of the egg, while the yolk, together with the residual 
protoplasm, is to be regarded as the vegetative pole. The animal pole at this 
stage consists of four segments or cells, while the whole of the vegetative pole 
has the value of one cell. The whole of the vegetative area may be compared to 
a gigantic fat cell in which the fat is replaced by food yolk. The function of 
the cortical protoplasm is to digest and absorb the food material as fresh 
nourishment is required by the growing organism. Having once grasped the 
significance of this point, the interpretation of future developmental phases does 
not present much difficulty. 

The ovum of an amphibian is holoblastic, while that of the herring is mero- 
blastic, yet this difference in the mechanical division of the ovum does not pre- 
vent a comparison of the two types. In an amphibian ovum, such as that of 
Rana, the majority of the germinal protoplasm has collected in the animal pole 
by the time that the first equatorial furrow is formed. The same is the case in 
the herring ovum. In Rana the vegetative pole consists at first of four large 
segments, which contain the greater portion of the yolk material, but which are 
also supplied with a considerable amount of protoplasm. The fact that at this 
stage the vegetative area consists of four segments instead of one, shows that 
the proportion of yolk to protoplasm is not so great as to entirely prevent the 
segmentation process from progressing. The proportion, indeed, is such that, 
in accordance with the law of segmentation, the division of the vegetative area 
is slower, and the resulting segments are larger, than is the case in the animal 
pole. It is also important to note, whilst making this comparison, that the 
protoplasm in the vegetative area of the amphibian ovum is not collected in any 
particular part, but that it is generally distributed throughout each segment. 
The same is the case with the yolk material. With further subdivision, there- 
fore, each cell in the yolk pole consists partly of yolk and partly of proto- 
plasm. 

Thus each cell carries its food supply along with it. Such is not the case 
in the herring ovum, and it is this fact which constitutes the essential difference 
between the two types. The food yolk in the herring ovum does not segment. 
This absence of segmentation in the yolk of fishes arises from two causes — 
viz., the overwhelming preponderance of food yolk, and the absence of a suffi- 
cient quantity of protoplasm distributed through it. In the herring ovum the 
protoplasm in the yolk pole consists of a comparatively thin cortical layer, with 
a few branching processes pressing into the food material, which are almost 
entirely confined to that portion of the vegetative area on which the archiblast 
rests. From the nature of this distribution, the food supply cannot be assimi- 



220 MR GEORGE BROOK ON THE 

lated in the same manner in the herring as it is in the amphibian ovum. In 
the herring the food yolk must be digested before it can be available as nourish- 
ment for the embryo. Had the separation of protoplasm from yolk been com- 
plete this end could not have been accomplished. It is therefore the function 
of the residual protoplasm in the yolk pole to make the food supply available for 
the use of the embryo. This is accomplished by a process which is essentially 
one of intracellular digestion, since the protoplasm in the yolk pole must be 
regarded as having the value of a cell, and is directly derived from the germinal 
area. The cortical protoplasm incorporates a portion of the yolk material 
within its substance, digests it, and thus adds to its bulk. A store of available 
material is thus laid up, which is utilised as occasion requires. It thus appears 
that the food yolk of the herring ovum is more nearly comparable in its manner 
of assimilation with the albuminous food supply of Lumbricus and some insects, 
than with the food yolk of the amphibian ovum. Nevertheless the yolk pole 
in the herring ovum has the same morphological value as that of the amphi- 
bian ovum, and it is mainly owing to the difference in distribution of the 
constituent parts that their subsequent behaviour is not identical. How far 
the tissues derived from each pole are identical in the two cases will be 
considered later. 

Although I am firmly convinced that in the herring ovum the third furrow 
is an equatorial one, I am not at present prepared to assert that this is the case 
m all fish ova. Nevertheless, it appears to me probable that an equatorial 
furrow will ultimately be shown to exist in all Teleostean ova at an earlier stage 
than has generally been supposed. 

To take the case of pelagic ova. In a paper on the development of Trachinus 
vipera (5) I have described the first furrow, which takes an equatorial direc- 
tion, to be the fifth of the series, and to be formed in the four central cells of 
the 16-cell stage when the 32-cell stage is being produced. I am now, however, 
inclined to think that I have neglected to observe one furrow altogether — that, 
namely, which divides archiblast from parablast. At the time the ovum is 
fertilised the yolk consists of one large yolk sphere and not of a number of 
small ones, as is the case in the herring ovum. There is also no appreciable 
increase in the quantity of germinal protoplasm after the egg is fertilised. The 
germinal protoplasm in the ripe unfertilised ovum consists of an even layer 
entirely surrounding the yolk. As the circumference of the yolk sphere is 
quite smooth, the line of demarcation between protoplasm and yolk is well 
marked. After fertilisation the bulk of the germinal protoplasm sinks to the 
lower pole of the ovum to form the germinal disc. A thin film of protoplasm 
is, however, still left surrounding the yolk, and this gets thicker towards the 
germinal area. The first furrow appears as a longitudinal depression across the 
centre of the circular disc, and is pushed down towards the yolk. A little later 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 221 

each end of the furrow becomes forked. The forked extremities then grow 
round, so that the two on each side meet. Two cells are thus formed, whose 
outline is very distinct in the region of the original longitudinal furrow, but gets 
more and more indistinct towards the periphery of the disc. The two cells thus 
formed do not enclose the ivhole of the protoplasm in the germinal area. The 
protoplasm at this stage has a yellowish tinge, and in the living egg the faint 
yellow shade can be seen to extend outside the limits of the two segmentation 
spheres (see figs. 1-4, loc. cit.). By another vertical furrow at right angles to 
the first the germinal disc becomes divided into four cells. It will be remem- 
bered that in the herring the first equatorial furrow simply completes the base 
of the four existing segmentation spheres, and that with the completion of this 
furrow there is a division into archiblast and parablast. In pelagic fish ova, 
however, the germinal disc rests directly on the yolk sphere, there being no 
intermediate area which is actively engaged in assimilation at this stage. Thus 
the base of the early segmentation spheres is not easily recognised. Only in 
that portion of the germinal disc which rests on the cortical protoplasm, and 
not on the yolk, could any such furrow be made out. There is, however, reason 
to suppose that the base of the first two segmentation spheres is not defined, 
and that even the lateral line marking their periphery does not reach the yolk at 
this stage, from the fact that the two cells increase considerably in size after 
their outline has been defined. At the completion of the 4-cell stage the 
segmented disc is undoubtedly divided off from the cortical protoplasm, and 
there is a division into archiblast and parablast, as in the herring ovum. 
Whether the furrow (or equivalent of a furrow) which brought about this 
separation was formed before or after the second meridianal furrow, I cannot 
say definitely at present. Whichever be the case, it is clear that this furrow is 
homologous with the third furrow in the herring ovum, and also with the third 
in the amphibian ovum. In the case of the Salmonidw, it appears to me also 
that the point which in reality corresponds with the first equatorial furrow in 
the amphibian ovum is reached at the 4-cell stage. When the base of these 
four cells comes to be defined there is still left a cortical layer of protoplasm, 
and a small quantity also mixed up with the yolk under the disc, as is the case 
in the herring ovum. 

From what has been already said, it will be seen that I conceive the term 
Archiblast to be applicable to that portion of the ovum which is usually spoken 
of as the germinal disc — that portion, namely, which is included in the early 
segmentation stages. It is for this reason that I have preferred to use the 
term germinal area in describing all changes in the herring ovum prior to the 
completion of the 4:-cell stage. The later stages of the segmentation process do 
not present any features of special interest. A stage in which the germinal 
disc consists of three rows of cells is shown in fig. 10. About 26 hours after 



222 MR GEORGE BROOK ON THE 

fertilisation a morula mass of cells has been produced, which is represented in 
fig. 12. It will be seen from the figure that the cells of the archiblast have 
already become differentiated into two well-marked groups. The outer row of 
cells are elongated and flattened, forming an epithelioid layer, whereas the 
remainder are comparatively large round cells, which are only loosely aggre- 
gated together. During the time that segmentation has been progressing in 
the archiblast the cortical protoplasm has increased considerably in bulk. In 
sections it may be seen that this layer gradually forms a thickening at the yolk 
pole. When the morula stage is reached the cortical protoplasm leaves the 
yolk pole, and gradually collects around and under the segmented disc. Even 
at a considerably earlier stage the cortical protoplasm may be seen to be 
accumulating towards the disc (see fig. 13, PI. XIV.); but after the morula stage 
is reached there is no longer any protoplasm to be observed at the yolk pole in 
the living egg. In stained sections there is always a thin film of protoplasm to 
be seen around the yolk spheres, and this is increased from time to time by the 
assimilation of more yolk. 

The collection of unsegmented protoplasm will be spoken of as the parablast. 
As will be seen later, the part played by what I term archiblast and parablast 
in the herring ovum is not identical with that which has been described by His 
and others in other forms, but I conceive the same terms to be applicable. 

The Part played by the Parablast. 

Historical. — The mode of origin of the parablast, and the part which it 
plays in the economy of the embryo, has during the past few years been one of 
the most keenly contested problems in this branch of embryology. In 1868 
His brought forward his well-known theory as to the development of the tissues 
in meroblastic ova (12). He held that in the chick the whole of the tissues of 
the future embryo were not derived from the three-layered blastoderm. That 
the blood and connective tissue series of structures arise independently of the 
segmented disc, and take their origin from the white yolk substance imme- 
diately underlying the blastoderm and outside the embryonic area. In their 
mode of origin the former set of tissues are known as archiblastic, and the 
latter as parallactic. According to His, the nuclei of the parablastic cells 
are derived from the white yolk spheres, which themselves have the value of 
cells. The segmented disc supplies the material for the three germinal layers, 
and the cells from the parablast find their way in between the cells of these 
layers. In the same year Kupffer (18) described in Teleostean fish ova a layer 
of protoplasm outside the germinal disc, in which, at the close of segmentation, 
concentric rows of free nuclei make their appearance. His investigations were 
made on Gasterosteus aculeatus, and other forms, and the following short 
extracts from his paper show the position taken up at the time : — " Man sieht 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 223 

rings urn den Rand des Keimliiigels Kerne auftreten, die in ganz 

regelmassiger Weise angeordnet sind. Es sind wasserklare, runde Blaschen, 
ohne irgend welche Komchen im Innern, die in concentrischen Kreislinien, auf 
das Centrum des Keimhiigels bezogen, sich gruppiren." " Man sieht namlich 
zwischen den blaschenartigen Kernen zarte Contouren auftreten, die genau an 
einander schliessende polygonale Felder umgrenzen, deren Mittelpuncte die 
Kerne einnehmen. Kurz es entsteht eine Lage eines regelmassigen, aus 

hexagonalen Zellen gebildeten Platten-epitheliums." " Unter den sich 

furchenden Keime ein besonderes Blatt sich bilde, das nicht aus den Fur- 
chungszellen herzuleiten ist, denn die Zellen desselben entstehen frei in einer 
den Dotter bekleidenden diinnen Blastemschicht, indem als Erstes die Kerne 
derselben erscheinen." " Ob dieses Blatt wirklich zum Darmdriisenblatt wird, 
muss dahingestellt bleiben, vielleicht ist es nur eine voriibergehende Bildung, 
was aber wohl unwahrscheinlich." 

So far as I am aware, this is the first clear account of a nucleated zone of 
protoplasm outside the segmented disc in Teleostean fish ovum. It is true that 
at an earlier date Lereboullet (21) observed a similar layer of cells in the 
egg of the pike, which he concluded was transformed into the lowest 
germinal layer. He was, however, of opinion that the cells were derived 
from small yolk spheres (globules vitellins), and failed to recognise the inde- 
pendent formation of the nuclei, which by Kupffer were ascribed to " free cell 
formation." 

So far as the Teleostei are concerned, the existence of this layer has since 
been thoroughly established. The points on which more recent investigators 
differ are firstly — the source from which the nuclei in this layer are derived; 
and secondly, the ultimate fate of the cells derived from it. 

Ten years ago Klein (16) made an important contribution to the subject, 
and reviewed the position taken up by earlier authors. This author concluded, 
from a study of the early stages of the trout, that besides the blastoderm 
proper, it is necessary to study closely the behaviour of the subgerminal and 
paragerminal substance, which " bears at all stages of development an im- 
portant genetic relation to the blastoderm and the embryo." Klein calls the 
segmented portion of the blastoderm archiblast, and the unsegmented portion 
in connection with the yolk is the parablast. I have followed Klein's nomen- 
clature in the present paper, although, as already pointed out, the terms are not 
used in the sense originally applied to them by His. The parablast layer was 
first correctly noted by Oellacher (23), who described it as continuous with 
the germinal disc in early stages, but mistook it for a vitelline membrane. 
Klein restricts the term parablast to the thickened welt of protoplasm, having 
a somewhat triangular section which forms a rim round the segmented blasto- 
derm in early stages. Van Bambeke (3) has described a similar layer in 

VOL. XXXIII. PART I. 2 H 



224 MR GEORGE BROOK ON THE 

Leuciscus, under the name of the " couch e interme'diaire." Klein and Van 
Bambeke differ considerably in their accounts of the early shape and position 
of this layer, but it seems probable that both authors are correct so far as the 
species studied is concerned, and that the parablast varies in position in 
different species and at different stages of development. Klein thus describes 
the appearance of nuclei in the parablast : — " Searching carefully through 
the parablast with a moderately high power (Hartnack's No. 8) we detect 
numerous isolated, small, transparent bodies, very faintly outlined, so as to 
be rendered just perceptible; between these and distinct nuclei all inter- 
mediate forms may be met with as regards general aspect, outline, and size. This 
obviously means new formation of nuclei. It therefore stands to reason to 
assume that, inasmuch as at a period when nuclei may be seen to multiply by 
division, the formation of nuclei de novo, as it were, still takes place in the 
parablast, the first nuclei of the 'parablast have also originated in the same 
manner, i.e., de novo." 

Klein is of opinion that the peripheral thickening of the archiblast is 
caused by an addition of cells from the subjacent parablast, and that a large 
part of the hypoblast is derived from this layer. The evidence of Van 
Bambeke also points to a similar conclusion. 

Kingsley and Conn (15) describe an " intermediary layer " in the pelagic 
ova of several fishes, in which " free cell formation " takes place, but are 
inclined to regard the true hypoblast as derived, in the first instance, from 
an invagination of the ectodermal layer of the epiblast. Mr Kingsley, how- 
ever, informs me that, since the publication of the paper referred to, he has 
been led to change his views on the subject. 

Hoffmann (14) affirms that the parablast arises with the formation of the 
first furrow, which takes an equatorial direction, thus dividing the germinal disc 
into two layers, each of which contains half of the first segmentation nucleus. 
According to this author, nuclei are abundant in the parablast during later 
stages, but the layer is not destined to take part in the formation of the 
embryo. The parablast, according to Hoffmann's view, is rather to be 
regarded as a degenerate relic of the vegetative pole in holoblastic types, 
which, owing to the increase of yolk, is no longer able to fulfil its former 
functions. 

According to Agassiz and Whitman (1), the nuclei found in the parablast 
(periblast) are derived from the margin of segmented blastoderm (archiblast), 
and these authors figure a sixteen-cell stage, showing the origin of the 
nucleated subgerminal layer. It would appear, however, from their observa- 
tions, that the parablast is not concerned in formation of the hypoblast, but 
that this is formed by a process of true invagination. 

Cunningham (8) supports the views of Agassiz and Whitman regarding 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 225 

the origin of the nuclei in the parablast, but is inclined to regard the 
hypoblast as resulting from an invagination of the outer, instead of the inner 
portion of the epiblast. Regarding the latter point, Cunningham may be 
said to stand almost alone in supporting Haeckel's view of the formation of 
the Teleostean gastrula, Kingsley, as already stated, having ceased to hold 
that view. The general question of the origin and significance of the pan- 
blastic layer in meroblastic ova has not received much attention in this 
country. Balfour (4 and 9), while accepting to a certain extent His's view 
as to the development of free nuclei in the surface yolk of Elasmobranchs, and 
in the white yolk underlying the blastoderm of the chick, does not accept his 
terminology. According to Balfour, a number of cells are formed in the upper 
strata of the yolk, which unite with the cells of the blastoderm during the 
processes of invagination and differentiation of the germinal layers, but these 
are apparently of only secondary importance. If the so-called " germinal 
wall " of the chick embryo is a portion of the layer here termed parablast, 
and there seems no room for doubt on this point, Balfour certainly held 
that certain portions of all the germinal layers may chiefly or partly be 
produced from this layer. Speaking of the differentiation of the layers in 
the area vasculosa of the chick, he says : — " The mesoblast and hypoblast of 
the area opaca do not arise by simple extension of the corresponding layers 
of the area pellucida ; but the whole of the hypoblast of the area opaca, and a 
large portion of the mesoblast, and possibly even some of the epiblast, take 
their origin from the peculiar material which forms the germinal wall, and 
which is continuous with the hypoblast at the edge of the area opaca." In 
his latest contribution to the parablast question, His (13) withdraws from the 
position which he formerly held in respect to the cellular character of the 
white yolk spheres, and consequently of the derivation of nuclei and cells 
from them. According to his view, the relation of the parablast to the 
embryo may be shortly summarised in the following manner : — The segmented 
blastoderm (archiblast) gives rise to the three primary germinal layers, 
epiblast, mesoblast, and hypoblast, but these only give rise to archiblastic 
tissues. 

The epiblast gives rise to the epidermis and the true glands derived from 
it, and to a part of the epithelium of the digestive tract, as well as to the 
nervous system. 

The hypoblast forms the rest of the epithelium of the digestive tract, and 
the glands belonging thereto. 

The mesoblast (or, more properly speaking, that portion of it which is 
derived from the archiblast) gives exclusively smooth and striped muscles, 
together with the epithelium of the urogenital tract. Mesoblast also gives 
r ise to the primitive clothing of the ccelom; but, according to His, this is 



226 MR GEORGE BROOK ON THE 

only transitory, and later another connective tissue covering takes the place 
of the primary one. 

The whole of the blood and connective tissue, in its widest sense, are 
developed at a later period outside the region of the segmented blastoderm, and 
are therefore parablastic in their origin. 

Thus the mesoblast in the ordinary sense (the middle germinal layer of 
Remak) is a compound, and not a simple layer, and the two portions may be 
spoken of as archiblastic and parablastic mesoblast. The parablastic mesoblast 
of His almost exactly corresponds with the mesenchyme of the brothers 
Hertwig (11). 

Finally, then, according to His, the parablast has nothing to do with 
the formation of the primary germinal layers, but is utilised later to form 
that portion of the mesoblast which gives rise to the blood and connective 
tissue series. 

More recently Waldeyer (26) has contributed a most important paper on 
the subject, which, I take it, goes to the root of the matter. Waldeyer calls 
attention to the structure of a typical meroblastic ovum, and to the relative 
distribution of protoplasm and yolk. The yolk is passive food material, which 
can only be utilised by the embryo after assimilation. Beneath the germinal 
disc there are a number of protoplasmic processes (Keimfortsatze) which press 
in amongst the passive food material ; and there is also a thin cortical film of 
protoplasm around the yolk. Segmentation takes place in the germinal disc, 
but does not affect the protoplasmic processes or the cortical layer. Later 
nuclei appear in the protoplasm, which is as yet unsegmented, and not in the 
yolk itself. The cells thus produced give rise to parablastic tissues. Thus the 
parablast layer is derived from the original protoplasm of the ovum, and not 
from white yolk cells, and its nuclei are also derivatives of the first segmenta- 
tion nucleus. Waldeyer distinguishes a primary segmentation, resulting in the 
formation of the archiblast, and a secondary segmentation, which frequently 
takes the form of budding, by which the parablastic tissues are derived. 
Waldeyer also points out that there is no essential difference between mero- 
blastic and holoblastic eggs ; but that throughout the animal kingdom a 
graduated series of modifications in the segmentation process are to be noticed, 
which are largely due to the varying quantity of passive food material contained 
within the ovum. It is also certain that the unequal distribution of the yolk is 
as important as its quantity in bringing about modifications in the segmentation 
process. According to Waldeyer's view, the formation of parablastic elements 
in holoblastic eggs is more easily explained than on His's view. During the 
segmentation process division takes place most rapidly in that part of the ovum 
containing least food yolk. At the base of the vegetative pole those cells are 
found which contain most yolk, and therefore segment more slowly. Those 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 227 

cells which are ready for tissue formation arrange themselves into the three 
primary layers, as in meroblastic ova, and constitute the archiblast. The cells 
not yet ready, and overladen with nutritive yolk, bud off later processes of 
protoplasm containing nuclei, which give rise to the parablastic elements of the 
embryo. 

Waldeyer admits that parablast cells may take part in the formation of 
the hypoblast in some forms, as has been maintained by so many authors ; 
but thinks its chief function in the higher vertebrates, at any rate, is 
to elaborate those cells which give rise to the blood and connective tissue 
elements. 

Kollmann (17) maintains that the layer which gives rise to the blood and 
connective tissues represents a distinct advance on the triploblastic arrange- 
ment of invertebrates, and raises it to the rank of a primitive organ under the 
name of acroblast, and gives it an equal value with the other germinal layers. 
He points out that acroblast exists in Aves and Lacerta as a peripheral 
thickening between the epiblast and hypoblast before the mesoblast (the 
archiblastic mesoblast of Waldeyer) is formed. The cells in this thickening 
give rise to a series of amoeboid wandering cells (poreutse) by division, and 
these in their turn fill in the serous cavities between the other germinal layers, 
and form the blood and connective tissue. 

My own Observations. — I will now describe the changes which take place in 
the parablast, as I have observed them in the herring and other forms. 

In the preceding section I described the appearance of the parablast at the 
end of what I consider the 'primary segmentation stage in the herring. The 
parablast, which has increased very considerably in bulk at the expense of the 
yolk, leaves the periphery, and collects mainly under the archiblast. About 
twenty-six hours after fertilisation transverse sections of the egg present the 
appearance shown in fig. 12. The archiblast has become differentiated into two 
layers. The outer small and somewhat flattened cells, which stain deeply with 
carmine, constitute the epidermal layer of the epiblast. The cells more centrally 
situated are larger, more rounded, and do not stain so deeply. They are loosely 
aggregated together, and represent the nervous layer of the epiblast in other 
Teleostean types which I have examined. It must, however, be remembered 
that we have not yet arrived at the invagination stage, and the germinal layers 
will not be differentiated for some time. Beneath the archiblast the parablast 
appears as a thick layer of protoplasm which is undergoing division into cells. 
Clear vacuole-like spaces are recognisable at irregular intervals both in the 
peripheral parablast and in the part more centrally situated. Around these 
clearer spots the protoplasm is becoming divided off so as to form a number of 
cells. The lines of fainter colour in the parablast represent the planes of 
division. So far as I can make out, there is no karyokinetic figure during 



228 MR GEORGE BROOK ON THE 

this process of cell formation in the parablast, and each nucleus arises inde- 
pendently of its neighbour, in a manner similar to that which I have described 
for Track inns. The observations of Kupffer, Klein, and others, are very clear 
on this point ; and I have frequently observed the full formation of nuclei both 
in the living Qgg and in the prepared material. The protoplasm in which these 
nuclei appear is, however, part of the original germinal layer of the ovum ; and 
it thus appears probable that they are to be regarded as derivatives of the first 
segmentation nucleus. I thus regard the cells formed in the parablast as 
secondary segmentation products in the sense of Waldeyer, and must leave 
the question of nuclei open until we have more detailed information on the 
subject. If, indeed, the observations of Hoffmann should prove true for all 
Teleostean fishes, the question presents no further difficulty ; but, as already 
stated, I have not been able to accept Hoffmann's views. 

The' cells thus formed in the parablast are next set free from their bed of 
unsegmented protoplasm, and join those derived from primary segmentation 
in the archiblast. About the same time the cells in the archiblast undergo 
division, and soon the cells derived from the parablast are no longer distin- 
guishable from the archiblast cells. As already stated, fig. 12 represents a 
section of an ovum of the herring twenty-six hours after fertilisation. In 
fig. 14, which is from material preserved two hours later, the cells derived 
from the archiblast are easily distinguished from those which have been 
recently added from the parablast. The archiblast cells stain more deeply, 
and besides nuclei there are indications of an intracellular reticulum. Perhaps 
the most noticeable characteristic is that the archiblast cells are loosely col- 
lected together, and present in section a number of vacuoles between adjoining 
cells which have not yet become completely separated. The parablast cells, on 
the other hand, only stain faintly, show little structure, and are closely crowded 
together beneath the others. In fig. 1(3, which represents the appearance two 
hours later again, all difference between the two sets of cells is lost, and if it 
had not been for the two previous stages, one would not have known that the 
archiblast had received any addition of cellular elements from the parablast. 
The unsegmented portion of the parablast still remains as a somewhat thin 
film beneath the segmented blastoderm, and again increases rapidly in bulk by 
assimilation of food yolk. Four hours later than fig. 15 a number of cells are 
again in process of formation, which are destined to be included in the seg- 
mented blastoderm in a similar manner to the first batch. Fig. 17 represents a 
section of this stage. The basal jiortion of the segmented blastoderm is repre- 
sented with its adjoining parablast. The two portions are not in contact at the 
periphery, but this is the result of a mechanical injury. An endeavour has 
been made to represent as nearly as possible the exact appearance and struc- 
ture of each cell in the portion of the section represented. A gradual transi- 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 229 

tion may be traced from the basal portion of the parablast, in which no nucleus 
is to be found, to the completely separated cells, which are already included in 
the morula. The first trace of cell formation is seen in a number of somewhat 
deeper stained patches of protoplasm, the colour getting more intense towards 
a centre, and gradually fading away from that point. A little later the cell 
contour becomes visible as a less deeply stained outline. In the next stage 
the nucleus appears as a less deeply stained portion in the centre of the cell. 
Its outline is almost circular, and a delicate more deeply stained reticulum 
may be observed in its interior. The deepest staining is noiv around the peri- 
phery of the nucleus, and the colour gradually becomes less intense towards 
the cell wall. Later the more deeply stained granules in the cell plasma 
arrange themselves in the form of a reticulum, which is ultimately connected 
with that of the nucleus. By this time the cells are indistinguishable from 
those already forming part of the morula. In some of the cells more trans- 
parent vacuole-like structures are found in the cell plasma*, both in the 
parablast cells and in those of the morula, but are much more numerous in 
the latter. Possibly these structures may be connected with the nourishment 
of the cell, but this is not clear. 

During the next few hours nearly the whole of the subgerminal parablast 
has been used up in budding off cells to join in the morula, which has in con- 
sequence increased very much in thickness, and presents a sharply curved 
upper surface. The subgerminal parablast in eggs forty-five hours after fer- 
tilisation consists of only a very thin film, as will be seen from fig. 18. The 
peripheral parablast, however, consists of a comparatively thick wedge-shaped 
mass, stretching from the base of the morula to the equator of the egg, and 
contains a considerable number of rows'of nuclei. This portion of the parablast 
has been gradually increasing in importance while the changes which I have 
just described have been taking place in the subgerminal parablast, but has not 
taken part in these changes. It is this peripheral portion of the parablast 
which has usually received attention from various investigators, and in which 
the development of nuclei has been so often observed in the living egg. The 
nuclei appear in concentric rings around the base of the morula, the first ring 
being formed in the thickest portion of the layer, i.e., the part immediately 
adjoining the morula. A faint cell outline can usually be observed in the proto- 
plasm around each nucleus, but after a time this appears to become obli- 
terated, though not so early as in Trachinus. In the living egg a single row of 
nuclei can be observed at a stage corresponding to fig. 12. At the stage 
shown in figure 14 there were three or four rows of cells in the peripheral 
parablast. In the living egg, of which fig. 18 is a section, the peripheral 
parablast has become cellular almost to the equator. The cells are arranged 
somewhat irregularly. In the portions more densely crowded with nuclei, the 



230 MR GEORGE BROOK ON THE 

cell outline is polygonal, ■whereas where there are fewer nuclei the cell contour 
is more rounded. So far as I am aware, this stage represents the earliest one 
at which cells from the parablast have been described as taking part in the 
formation of the embryo in other Teleostean types. It corresponds to that of 
fig. 2 in my account of the pseudo-invagination in Trachinus (6). The 
extension of the morula over the yolk, the formation of the segmentation 
cavity, and the differentiation of the germinal layers has not yet commenced, 
though these changes immediately follow on this stage. So far as my investi- 
gations go, I am not aware of any case exactly comparable with this, though 
further investigations may probably reveal such. In all the Teleostean types 
with which I am acquainted, with the exception of the herring, the primary 
segmentation process results in the formation of a morula corresponding to 
that of fig. 18, and it is only in stages immediately following this that the 
elements resulting from secondary segmentation take part in the further 
differentiation of the blastoderm. In other words, in most Teleostean ova, the 
morula consists solely of archiblastic elements, and it is only after the formation 
of the segmentation cavity, and the commencement of invagination, that the 
parablastic elements come to be utilised. In the herring, as we have seen, at 
least two distinct batches of parablast cells are budded off, and unite with those 
of the archiblast before any trace of differentiation of the morula is to be found. 
The final morula in this case contains parablastic as well as archiblastic 
elements. The difference is important, and as I hope to show later, is con- 
nected with the early elaboration of the parablast, and probably also with the 
absence of a vitelline circulation in this type. 

Shortly after the stage represented in fig. 18 the morula begins to spread 
out over the yolk, and the extension is accompanied by a thinning out of the 
central portion, which has hitherto been thickest. In this way a segmentation 
cavity is formed, which, however, never reaches so important a development 
in the herring as in some other Teleostean types. The parablast forms the 
floor of the segmentation cavity, while the cells of the morula form its roof and 
lateral boundaries. Fig. 21 (PI. XV.) represents a longitudinal section in the axis 
of the embryo 68 hours after fertilisation. The roof of the segmentation cavity 
is formed of several rows of cells, the most external constituting the epidermal 
layer of the epiblast. Towards the periphery of the blastoderm there is a 
thickening forming the commencement of the blastodermic rim. There is no 
invagination of the epidermal layer of the epiblast, but the thickening may 
possibly be in part produced by an invagination of the nervous layer. I am, 
however, inclined to believe that the thickening, in so far as it does not result 
from an addition or segregation of cells from the parablast, is due to mechanical 
agencies. As the cells forming the roof of the segmentation cavity press 
towards the periphery, so as to aid the blastoderm in its extension over the 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 231 

yolk, they would naturally form a thickening on the under surface. The floor 
of the segmentation cavity is lined by a comparatively thick layer of para- 
blast, in which a number of free nuclei are embedded. The parablast 
extends under the thickened peripheral portion of the blastoderm, and 
around its margin forms a thickened welt, in which a number of nuclei are 
also found. 

Fig. 22 represents a portion of the section more highly magnified, The 
peripheral parablast is richly charged with nuclei, as also is that lining the 
floor of the segmentation cavity. These nuclei, before the formation of the 
peripheral thickening, were abundantly distributed throughout the parablast, as 
may be seen by a reference to fig. 20, which represents a slightly earlier 
stage. Now, however, the portion of the parablast on which the thickened rim 
rests is very thin, and is quite devoid of nuclei, whereas both in the peripheral 
parablast and in that portion in front of the thickening nuclei are still nume- 
rous. It is, therefore, impossible to avoid the conclusion that the nuclei, and 
a large portion of the protoplasm formerly situated in the region of the 
thickened rim have been used up in the formation of that thickening. The 
layer, which is pushed inwards from the thickening, constitutes the primitive 
hypoblast, so that I am brought back to my former observations on the 
development of Trachinus and Motella (6), and can only reiterate that this 
layer is mainly if not entirely formed by a segregation of cells from the para- 
blast. A study of fig. 22 also brings out another important point. The cells 
of the morula rest directly on the parablast in the region of the blastodermic 
rim, whereas the two layers are separated more centrally by the segmentation 
cavity. The result is, that the primitive hypoblast is closely connected with 
the epiblast of the morula in the blastodermic rim, whereas the layer as it 
gradually fills in the segmentation cavity never adheres to the epiblast, but is 
always distinctly separated from it by a slight remnant of the cavity itself. It 
is in this manner that I would propose to get rid of one of the chief arguments 
against the parablastic origin of the primitive hypoblast. It has been argued 
by Henneguy (10) and others, that if the primitive hypoblast in Teleosteans 
was really formed from a different source than the archiblast, the two primary 
layers ought to be distinct throughout their entire length. In other words, that 
the separation of the primitive hyploblast and epiblast towards the centre of the 
embryonal shield, and their close union at the periphery, was a strong argu- 
ment in favour of the origin of the primitive hypoblast as a true invagination 
of the archiblast. Hoffmann holds similar views. It will, however, be easily 
understood that this close union of the primitive layers at the periphery is 
equally the necessary result of the views which I advocate. The segmentation 
cavity does not extend across the whole diameter of the disc as was advocated 
by Haeckel, but the peripheral portion of the disc always rests on the para- 

VOL. XXXJII. PART I. 2 T 



232 MR GEORGE BROOK ON THE 

blast for about l-6th of its diameter. It is exactly in this part, and in this 
part only, that the two layers are originally in close union. 

I need not describe in detail the further advance of the primitive hypoblast, 
and the gradual obliteration of the segmentation cavity as the result. Through- 
out the process the parablast is very active in its elaboration of food yolk, and 
is continually supplying the new layer with more cells. Fig. 23 represents a 
transverse section of the body axis at a considerably later stage. It shows the 
primitive hypoblast in close union with the parablast, from which it is derived, 
but almost completely separated from the cells forming the roof of the 
segmentation cavity. Fig. 24, which is a more highly magnified view of a 
portion of this section, shows several important points. The intimate con- 
nection between yolk and parablast cannot fail to be noted, and the physiolo- 
gical function of the layer — the elaboration of fresh material for the embryo — 
is well. brought out. The upper portion of the parablast contains a large 
number of free nuclei, which agree in every particular with the nuclei of the 
primitive hypoblast cells. Around some the protoplasm is seen to be con- 
stricted off to form cells. These are seen in all stages, from those completely 
embedded in unsegmented protoplasm to those adhering to the parablast only 
at one point. 

Although at some points the epiblast and the primitive hypoblast are in 
contact owing to the rapid and prolific growth of the latter, it appears probable 
that the cells situated above the segmentation cavity give rise to the epiblast 
only. While the primitive hypoblast remains still undifferentiated, the cells of 
the epiblast collect, especially in the head region, forming a special thickening 
for the rudiment of the central nervous system. In the axis of the embryo the 
primitive hypoblast in the region of the head is pushed to each side by this 
enormous development, so that, in longitudinal section, the primitive hypoblast 
appears to cease in the posterior portion of the head swelling. Such a section 
is shown in fig. 25. The nuclei in the parablast are still prominent, and the 
two primitive layers are separated by a small space in the neck region, but are 
united towards the caudal extremity. Fig. 26 represents a portion of the 
section situated near the tail swelling, more highly magnified. The cells in the 
epiblast are closely packed together, whereas those in the primitive hypoblast 
are more loosely arranged. The two layers are not, however, distinctly 
separated, though a difference in the staining of the nuclei indicates the point 
of union of the two layers. The parablast still persists as a thin, unsegmented 
layer of protoplasm closely connected with the yolk, in which numerous free 
nuclei are embedded. 

At a later stage in transverse section (fig. 30), the primitive hypoblast cells 
in the median line change their appearance considerably. A number of cells, 
forming a somewhat circular or slightly quadrate cord, lose their distinct 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 233 

outline, and seem to fuse together to form a more solid mass. This is the 
commencement of the notochord. The two lateral portions become separated 
from it as the lateral mesoblastic plates, and a single row of cells remains in 
connection with the parablast, which constitute the commencement of the 
permanent hypoblast. The lateral plates of mesoblast are completely separated 
from the epiblast, but above the notochord there is an arrangement of the cells 
which would lead one to suppose the two had been in close union. It thus 
appears that in the herring the three germinal layers are not completely 
differentiated until the notochord has made its appearance to separate the two 
lateral plates of mesoblast. Though I cannot speak with absolute certainty, 
there appears every probability that the primitive hypoblast gives rise to 
notochord, mesoblast, and permanent hypoblast, and that the morula mass of 
cells existing prior to the formation of the primitive hypoblast (the archiblast 
in other Teleostean types) persists as the epiblast. It is possible, however, but 
by no means sure, that some of its cells are included in the upper rows of 
mesoblast cells. 

Theoretical Considerations. — Since my observations were completed and the 
bulk of the present paper written, I have received a paper by Dr Ruckert (25) 
on the Formation of the Germinal Layers in Elasmobranchs, published about 
six months ago, in which the author has come to very similar conclusions to 
those here advocated. His observations were made chiefly on the eggs of 
Torpedo, and the following is a short summary of the results arrived at : — 

1. The free nuclei in the yolk of meroblastic eggs (which Ruckert terms 

merocytes) are segmentation products which have undergone a secondary 
modification under the influence of the food yolk. Their mode of origin 
is most clearly demonstrated by the peculiar segmentation of the richly 
deutoplasmic but still holoblastic eggs of many invertebrates (Insecta, 
Crustacea, Vermes). In these there is at first a total segmentation, but 
later the nuclei in the vegetative pole, together with the surrounding- 
protoplasm, separate themselves from the deutoplasm, and while under- 
going frequent division produce embryonal cells which are undistinguish- 
able from those formed by regular segmentation. The deutoplasm in 
the vegetative pole becomes by this means passive food material, and the 
whole original holoblastic egg a meroblastic one. 

2. In Elasmobranchs the merocytes are amoeboid (rhizopodenartig) structures 

whose richly ramifying processes absorb and assimilate the surrounding 
yolk. They produce later a number of embryonal cells by endogenous 
cell formation or budding. 

3. The embryonal cells produced from merocytes take part in the formation 

of all the germinal layers. In most animals they form the entoblast, 



234 MR GEORGE BROOK ON THE 

mesenchym, and the blood. In many Arthropods they likewise supply 
the entire ectoblast. 

4. In Elasmobranchs they play only a subordinate part in the formation of the 
ectoblast, and must here probably be regarded as homologous with the 
vegetative pole of holoblastic eggs. 

."). The merocytes arise with the first equatorial division of the segmenting 
ovum. The germinal disc which represents the animal pole goes on 
segmenting. The merocytes increase only to a trifling extent during 
this period. The blastula cavity appears between the morula (archi- 
blast) and the superficial layer of yolk charged with merocytes — that is 
to say, between the animal and the vegetative poles of the egg. Its roof 
gives rise to the ectoblast ; its floor supplies the ectoblast in the follow- 
ing manner : — The embryonal cells formed from the merocytes are 
pushed up into the blastula cavity from the yolk, and close its lumen. 
This process commences all around the periphery of the disc, but is later 
mainly confined to the posterior position (embryonal shield). The blood 
and mesenchym cells also arise from merocytes. 

It will thus be seen that, according to Ruckert, the hypoblast is derived 
mainly from merocytes and not from a rearrangement of the " lower layer cells " 
of the primary segmentation, as has been maintained by previous authors. The 
merocytes of Ruckert undoubtedly corresponds with the free nuclei in the 
layer which I have termed parablast, and indeed in the Trout there is an 
approach to the structure described by Ruckert. 

If these observations are correct, it will be necessary to modify considerably 
our ideas of a meroblastic egg. Although meroblastic ova are usually regarded 
as having been derived from holoblastic ones by the inclusion of an excess of 
passive food yolk, the two appear to be more closely related than has generally 
been admitted. We have been in the habit of regarding segmentation as only 
taking place in the germinal disc, and have usually derived the three primary 
germinal layers as a result of this segmentation process. The yolk is therefore 
in the main regarded as a passive food store, which is assimilated later through 
the digestive and circulatory systems. Waldeyer's idea of the interrelation of 
archiblast and parablast certainly modifies this view, and, I take it, is a step in 
the right direction. According to the views here advocated, a meroblastic egg 
produces the germinal layers from both animal and vegetative poles of the 
ovum, as is the case in holoblastic ova, but the means by which this end is 
attained is different in extreme cases. As Ruckert has, however, pointed out, 
there are a large number of types, particularly amongst the Arthropods and 
Mollusca, which, so to speak, bridge over the gap between the two extremes. 
The difficulty lies in the proper understanding of the vegetative pole in mero- 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEL 235 

blastic ova. As already pointed out, the vegetative pole in a Teleostean such as 
the herring consists at first of only one cell, or if it contains more than one 
nucleus the protoplasm is at any rate unsegmented. The protoplasm is mainly 
peripheral, and surrounds a practically solid mass of passive yolk. There are at 
most a number of protoplasmic filaments pressing down amongst the yolk 
spherules which serve to bring the active and passive material into closer union. 
Too much stress cannot be laid on this fact, for to my mind it constitutes the 
main difference between meroblastic and holoblastic ova. A certain proportion 
of yolk to protoplasm may or may not prevent total segmentation, the result 
depending on their relative distribution in the ovum. 

The development of the Decapod Crustacea shows that, to commence with, 
total segmentation may take place, and then that later a central unsegmented 
yolk mass may be formed, while the protoplasm and nuclei accumulate on the 
surface. This appears best explained by supposing that the protoplasm, when 
generally distributed throughout the yolk, was present in sufficient quantity to 
bring about total segmentation, but that, as it collects at the surface, a central 
mass of practically pure yolk is formed, which can no longer be assimilated in 
the same manner as that in a typical holoblastic egg such as that of Amphioxus. 
In this manner an ovum at first holoblastic becomes secondarily meroblastic. 
To return to our Teleostean ovum. The protoplasm in the vegetative pole 
increases rapidly in bulk by an assimilation of its enclosed food material, and 
thus is enabled to bud off cells which, had the distribution of yolk and 
protoplasm been otherwise, would have been produced by normal segmentation. 
Thus arises the distinction between primary and secondary segmentation, and 
the latter is seen to be only a modified form of the former. The first equatorial 
furrow, whenever it arises, divides the animal from the vegetative pole, and in 
meroblastic ova the segmentation in the vegetative pole, by becoming of the 
secondary type, accommodates itself to any relative proportion of yolk. 

According to my observations, the separation of the animal from the 
vegetative pole in the herring occurs with the formation of the third furrow. 
It may be, however, that this is not the case in all other Teleosteans. I never- 
theless regard the furrow or partial furrow which divides the peripheral proto- 
plasm from that which undergoes primary segmentation in the germinal disc, as 
the equivalent of the first equatorial furrow in holoblastic types. 

The archiblast in the herring, together with the cells derived from the 
parablast, prior to the formation of the segmentation-cavity, give rise to the 
epiblast. The vegetative pole then gives rise to the primitive hypoblast, which 
is in turn differentiated into the mesoblast and permanent hypoblast. I am 
not at present prepared to say whether this is the case in most of the 
Teleosteans. It appears, however, on a priori grounds, that at any rate in 
those forms which have a vitelline circulation the process may be modified. It 



236 MR GEORGE BROOK ON THE 

may be that in such types the parablast is mainly concerned in the formation 
of the connective-tissue elements, and so cannot play so important a part in 
the formation of the germinal layers. In higher vertebrates {e.g., the chick) 
the mesoblast in connection with the primitive streak is probably formed 
independently of the parablast, but it is generally admitted that the hypoblast 
is in part formed from that layer. So far as the chick is concerned, there 
appears little doubt that the blood and connective-tissue elements are derived 
from the parablast, and further investigation may show that in the trout and 
allied types there is a similar double origin of the mesoblast. One further 
point remains to be noted. The primitive hypoblast, as I have observed it in 
the herring, is precisely homologous with that of the Amphioxus, which, be it 
remembered, is a holoblastic type. In both cases the primitive hypoblast 
becomes differentiated into two lateral plates of mesoblast separated by the 
notochord, and what remains constitutes the permanent hypoblast. 



LIST OF LITERATURE REFERRED TO IN THIS PAPER. 

1. Agassiz and Whitman. On the Development of some Pelagic Fish Eggs, Proc. Amer. Acad, of 

Arts and Sci, vol. xx. 1884. 

2. Boeck. Om Silden og Sildefiskerierne, &c, Christiania, 1871. 

3. Van Bambeke. Recherches sur l'Embryol. d. poissons osseux, Acad. Roy. d. Belgique, Bruxelles, 

1876. 

4. Balfoub, F. M. Treatise on Comp. Embryology, 2 vols., London, 1880-81. 

5. Brook. Prelim. Account of the Devel. of Trachinus vipera, Jour. Linn. Soc. (Zool.), vol. xviii., 

1884. 

6. Brook. On the Origin of the Hypoblast in Pelagic Teleostean Ova, Quart. Jour. Micr. Sci., Jan. 

1885. 

7. Brook. Experiments with Herring Ova, Report of Fishery Board for Scotland. 1885. 

8. Cunningham. On the Relation of Yolk to Gastrula in Teleosteans, Quart. Jour. Micr. Sci., 1885. 

9. Foster and Balfour. Elements of Embryology, 2nd edition. 

10. Henneguy. Prem. phenom. d. d^veloppement d. poissons osseux, Bull. Soc. Phil, de Paris, 

1880 (see also second notice in Comptes Rendus, xcv. 1882). 

11. Hertwig, 0. & R. Die Coelom-theorie, Jena, 1881. 

12. His. Entw. des Hiihnchens, Leipzig, 1868. 

13. His. D. Lehre v. Bindesubstanzkeim (Parablast), Archiv f. Anat. u. Phys. (Anat. Abtheil.), 1882. 

14. Hoffmann. Z. Ontogenie d. Knochenfische, Amsterdam, 1881. 

15. Kingsley and Conn. Some Obs. on the Embryology of the Teleosts, Mem. Boston Soc. Nat. 

Hist., 1883. 

16. Klein. Obs. on Development of Common Trout, Quart. Jour. Micr. Sci., 1876. 

17. Kollmann. D. Randwulst u. d. Ursprung d. Stutzsubstanz, Archiv Anat. u. Phys. (Anat. 

Abthiel.), 1884. 

18. Kupffer. Z. Entw. d. Knochenfische, Archiv Milcr. Anat., Bd. iv., 1868. 

19. Kupffer. Z. Entw. d. Herings im Ei, Jahresb. d. Comm. z. Wis. Unters. d. deutschen Meere, 

1874-76, Berlin, 1878. 

20. Kupfker. U. Laichen u. Entw. des Herings, Ibid. 

21. Lereboullet. Rech. d'Embryol. comp. sur 1. develop, de la Truite, d. Lezard et d. Limn^e, Ann. 

Sci. Nat., series iv. vol. xvi., 1861. 

22. Meyer. Beob. ii. Wachsthums d. Herings, Jahresb. d. Comm. $c, 1874-76, Berlin, 1878. 

23. Oellacher. Entw. d. Knochenfische nach Beobacht. am Bachforelle, Zeii. Wiss. Zool., xxii. xxiii. 

1872-73. 

24. Ryder. Embryography of Osseous Fishes, Report U.S. Fish. Comm. 1882, Washington, 1884. 

25. RCckert. Z. Keimblattbildung bei Selachicrn, Miinchen, 1885. 

26. Waldeyer. Archiblast u. Parablast, Archiv Milcr. Anat., xxii., 1883. 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 237 



EXPLANATION OF PLATES. 

Figures 5, 7, and 8 are taken from drawings by my friend Mr W. L. Caldekwood ; figures 6 and 
9 were originally drawn from the living egg, and the colours are diagrammatic. All the other figures 
were drawn for me by Mr J. T. Thompson, M.B., CM. I feel it only just to Mr Thompson to state 
that much of the delicacy of his original drawings has been unavoidably lost in their reproduction on 
stone. The figures are taken exclusively from ova of herring. 

Plate XIII. 

Fig 1. — Section of viscous layer and egg-membrane of a ripe unfertilised ovum. Externally is seen the 
homogeneous viscous layer, then follows the outer layer of zona radiata longitudinally 
striated, and most internally is the inner layer of zona radiata transversely striated. 
Gundlach, j^, Oc. 3. 

Fig. 2. — Section of abnormal egg-envelopes, showing viscous layer divided into two strata, and each 
exhibiting a well-marked transverse striation. Gundlach, ^ F , Oc. 3. 

Fig. 3. — Transverse section of an unfertilised ovum. The carmine-stained protoplasm is seen distri- 
buted throughout the yolk, and not collected into a definite layer. In its meshes lie the 
large unstained yolk-spheres, and they occupy the greater portion of the egg. Lying imme- 
diately beneath egg-membrane are seen smaller yolk granules. Swift, 1 inch. 

Fig. 4. — Germinal vesicle of ovarian ovum. Latest stage observed. Shows the irregular, somewhat 
quadrangular, outline, the fine protoplasmic threads leaving its margin and going into yolk- 
mass, and the delicate nuclear reticulum. Gundlach, ^. 

Fig. 5. — Section of an unfertilised ovum after lying two days in sea- water. Differs only from recently- 
matured ovum in that the protoplasmic network has withdrawn a little from centre of egg, 
and there is rather more protoplasm at periphery, but no disc-like prominence is to be 
seen. Zeiss, A A, Oc. 3. 

Fig. 6. — Optical section of a living egg, one hour after fertilisation. Germinal protoplasm is seen 
collecting at circumference as a continuous layer, considerably thicker at one side. Yolk 
granules are no longer visible. There is a large breathing-chamber. Zeiss, A A, Oc. 3. 

Fig. 7. — Actual section of an ovum, one hour after fertilisation. Shows true relation of the protoplasm 
to the yolk. The protoplasm is collecting at surface, but there is still left a portion mixed 
amongst the yolk-spheres in the shape of branching processes, which towards germinal pole 
are stronger, and penetrate further into yolk. Zeiss, A A, Oc. 3. 

Fig. 8. — Section of an egg, five hours after fertilisation. Germinal protoplasm has almost entirely 
collected at germinal pole. Large masses of yolk are entangled in the meshes of its 
processes, and a number of yolk-masses, varying in size, are also found in body of germinal 
mound itself. Zeiss, A A ; Oc. 3. 

Fig. 9. — Egg, nine hours after fertilisation ; four-cell stage. Sketched from living egg, and coloured 
to harmonise with the other figures. Shows the separation of parablast from archiblast 
by the formation of an equatorial furrow. Lacunae are indicated in the yolk, which are 
continued towards the base of disc by stalks. Swift, 1 inch. 

.Fig. 10. — Section of egg, twenty-one hours after fertilisation. Three rows of cells are seen in germinal 
disc. Cell reticulum is well brought out by differential carmine stain. Zeiss, A A. 

Fig. 11. — Section of egg, twenty-four hours after fertilisation, showing morula shortly before addition of 
cells from parablast. The protoplasm of parablast is chiefly situated at yolk pole at this 
stage. Zeiss, A A. 



238 MR GEORGE BROOK ON THE 

Fig. 12. — Section of egg, twenty-six hours after fertilisation. Morula mass of cells (primary morula). 
An outer row of flattened epithelioid cells is differentiated = epidermal layer of epiblast of 
authors. Remaining mass consists of rounded cells loosely aggregated = nervous layer of 
epiblast of authors. Cortical protoplasm has left yolk pole to collect under and around 
segmented disc and nuclei, and outlines of cells can he made out in the subgerminal para- 
blast. Primary segmentation has ended, and secondary segmentation has begun. Section 
is not quite through centre of egg. Zeiss, A. A. 



Plate XIV. 

Fig. 13. — An imperfect section of a stage shortly before that of fig. 12. Parablast is collecting towards 
disc. Zeiss, A A. 

Fig. 14. — Egg, twenty -eight hours after fertilisation. Section through marginal part of morula (haema- 
toxylin). Cells from archiblast easily distinguisbed from those which have been recently 
added from the parablast. Archiblast cells are stained more deeply, and there are 
indications of intracellular reticulum. Numerous vacuoles are seen between archiblast 
cells and bridges of protoplasm connecting the neighbouring cells together. Zeiss, D D. 

Fig. 15. — Section of an egg, thirty hours after fertilisation. Unsegmented portion of parablast is seen 
as a thin film beneath the segmented disc. End of first budding-off process in parablast. 
Swift, 1 in. 

Fig. 16. — Margin of morula of a stage about same as fig. 15, more highly magnified to compare 
with fig. 14. All distinction between the two kinds of cells is lost (lueniatoxylin). 
Zeiss, D. D. 

Fig. 17. — Egg, thirty-four hours after fertilisation. Section represents basal portion of disc with the 
adjoining parablast ; the two portions are not in contact at periphery, but this is the result 
of a mechanical injury. Cells are again to be seen in process of formation in the parablast. 
Differential carmine staining shows gradual transition from cells in process of formation at 
the base of the parablast, to those already included in the germinal disc. Swift, A 

Fig. 18. — Section of egg, forty-five hours after fertilisation. The final morula, containing in herring 
parablastic as well as archiblastic elements. Subgerminal portion of parablast is only a 
thin layer, peripheral portion, however, forms a thick wedge-shaped mass, extending from 
base of morula to equator of egg, and contains a considerable number of nuclei. Swift, 1 in. 

Fig. 19. — Right corner of morula of fig. 18, more highly magnified and showing the nuclei in the 
peripheral parablast. Swift, A. 

Fig. 20. — Section of egg, fifty-six hours after fertilisation, showing beginning formation of segmentation- 
cavity. Parablast forms its floor, and the cells of the morula form its roof and lateral 
boundaries. Nuclei are seen to be distributed throughout the parablast. Swift, 1 in. 

PlATE XV. 

Fig. 21. — Longitudinal section of disc 'n axis of embryo, sixty-eight hours after fertilisation. Shows 
roof of segmentation-cavity formed of several rows of cells, its floor of parablast. Thicken- 
ing at periphery forms commencement of blastodermic rim, and the layer pushed inwards 
from this thickening constitutes primitive hypoblast. Swift, 1 in. 

Fig. 22. — More magnified view of a portion of fig. 21. Absence of nuclei in thinned out portion of 
parablast immediately below rim, but they are still numerous in peripheral parablast, and in 
parablast forming door of segmentation-cavity. In region of blastodermic rim the cells of 
the morula rest directly on the parablast ; but centrally the two layers are separated by 



FORMATION OF THE GERMINAL LAYERS IN TELEOSTEI. 239 

the segmentation-cavity. Hence the close union of the primitive layers at periphery of 
disc. Swift, i. 

Fig. 23. — Transverse section through axis of embryo, 77£ hours after fertilisation. Shows primitive 
hypoblast in close union with parablast, from which it is derived, but almost completely 
separated from the cells forming roof of segmentation-cavity. Swift, 1 in. 

Fig. 24. — More highly magnified portion of fig. 23. Shows the intimate connection between yolk and 
parablast. Upper part of parablast contains a number of free nuclei, agreeing in every 
particular with the nuclei of the primitive hypoblast cells, and around some of them proto- 
plasm is constricted off to form cells. Zeiss, E. 

Fig. 25 — Longitudinal section, in axis of embryo of an egg, 92| hours after fertilisation. Blastopore 
is near its closure. Primitive hypoblast appears to cease at posterior portion of head 
swelling, due to its being in this region pushed to each side by the enormous development 
of rudiment (keel) of central nervous system. Nuclei are still prominent in the parablast, 
and the two primitive layers are separated by a small space in neck region, but are united 
towards caudal extremity. Swift, 1 in. 

Fig. 26. — Shows a portion of fig. 25, in region of tail swelling, more highly magnified. Cells in epiblast 
are closely packed together, whereas those of primitive hypoblast are more loosely arranged. 
The two layers are, however, not distinctly separated, though a difference in the staining of 
the nuclei in the original preparation indicates point of union of the two layers. Parablast 
shows as a thin unsegmented layer of protoplasm, in which are embedded numerous nuclei. 
Zeiss, D. I). 

Fig. 27. — Longitudinal section in axis of embryo, 101 J hours after fertilisation. Blastopore is just 
closed. Nervous epiblast is conspicuous in anterior region. Mesoblast is beginning to 
show division into somites, and hypoblast is distinctly separated in region of somites. 
Zeiss, A A. 

Fig. 28. — More highly magnified portion of same embryo, as fig. 27, showing epiblast, mesoblast, and 
hypoblast, the last still in connection with the unsegmented protoplasm of the parablast. 
Zeiss, D D. 

Fig. 29. — Transverse section through body axis of an embryo of same stage as figure 27. Upper part of 
section passes through the head region, and shows the thickened nervous epiblast (keel). 
Lower part passes through tail region ; notochord not yet differentiated. Zeiss, A A. 

Fig. 30. — Transverse section of an embryo, 112 hours after fertilisation. Shows separation of the 
notochord and the two lateral mesoblastic plates. A single row of cells remains in con- 
nection with the parablast, and constitutes the rudiment of the permanent hypoblast. 
Zeiss, A A. 



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( 241 ) 



X. — On the Structure of Suberites domuncula, Olivi (0. S.), together with a 
Note on peculiar Capsules found on the surface of Spongelia. By J. 
Arthur Thomson. (Plates XVI., XVII.) 

(Read 7th June 1886.) 

Part I. 

The sponge Suberites domuncula attracted the attention of the Italian 
naturalist Olivi* almost a hundred years ago, but was on account of its firm 
india-rubber like consistency erroneously regarded as an Alcyonium. Beyond 
the general diagnosis of NARDot who erected the genus Suberites, the struc- 
ture of the sponge has, I believe, remained virtually unknown. Not for this 
reason, however, but because the Monaxonia in general, of which Suberites is 
an example, are still for the most part but little known, Prof. F. E. Schulze 
of Berlin was good enough to ask me last winter to investigate the structure 
of this sponge. To him, therefore — perhaps the greatest living authority on 
the subject — I may be allowed to express my gratitude for the hospitable 
reception with which he welcomed a stranger to his laboratory, and for the 
constant interest and assistance with which he encouraged my work. That I 
have not succeeded in giving a perfect elucidation of the structure is largely 
due to the same cause which has kept it for so long almost wholly unknown. 
The crowded siliceous spicules, the compact consistence, the smallness of the 
ciliated chambers, make the histological analysis somewhat difficult. Such 
gaps as exist in my investigation I hope to be able to fill up by the study of 
related forms, and have with that end begun the study of Suberites mana. 

Suberites domuncula is found covering the outside of a sea-snail shell, 
inhabited by a hermit crab. The change of position thus secured for the 
sponge is an obvious advantage of this commensalism, while the hermit- 
crab on the other hand is very effectively masked. Numerous polypes are also 
found embedded in the sponge. In none of the forms which I had the oppor- 
tunity of examining was the hermit crab present, and in all the limy shell was 
to a greater or less extent eaten away, leaving in one instance only the apex. 
How the lime is precisely affected I was not able to discover. The cavity 
remaining after the shell has gone leaves a wide coiled canal, which will 
doubtless aid in the irrigation of the compact mass. 

My material was obtained from the Berlin Aquarium, and after careful 
dehydration, was stained (generally with alum carmine or hematoxylin), and 
* Bronn's Klassen und Ordnungen, Vosmaer " Porifera," p. 33, t i&*&, P- 332. 

VOL. XXXIII. PART I. 2 L 






242 MR J. ARTHUR THOMSON ON THE 

sectioned in the usual fashion. I found it useful for general survey to make 
several large sections through the sponge. 

The ectoderm of Suberites exhibits no marked peculiarities, but consists of 
a fine layer of small polygonal and apparently unequal cells, the contours of 
which were readily demonstrable by the silver nitrate or gold chloride method. 
With a lens the skin can be seen to be covered with fine pores, while numerous 
larger apertures are irregularly distributed over the surface. I was, however, 
unable to discover any oscular opening or openings. The larger apertures 
seemed, on closer examination, to be widened canals occupied by the abundant 
commensal polypes. Between the pores the points of the monact spicules 
projected slightly above the surface. 

Not a little of the difficulty attending the investigation of Suberites is clue 
to the very abundant occurrence of the large free siliceous needles. On a section 
through the whole sponge a radiate disposition can be recognised. They 
extend in large crowded brush-like bundles from the centre outwards, though 
considerable irregularity of arrangement is also observable. The brush-like 
bundles are best seen towards the surface between adjacent canals. The 
needles exhibit a simple unaxial form, running to a point at one end, and 
knobbed like a pin at the other (Plate XVI. fig. 4). I also observed a diact 
form, with double median nodes and with both extremities pointed, a modifica- 
tion readily derivable by fusion or doubling. 

The Ciliated Chambers (fig. 4). — The disposition of the ciliated chambers, which 
is of course the principal point, is very difficult to determine owing to the number 
of spicules, the compactness of the sponge, the minuteness of the chambers 
themselves, and the adjacent relations of afferent and efferent canal systems. 
In sections of fortunate thickness and staining, the small chambers can be seen 
throughout the whole sponge, but more abundantly towards the periphery. 
They seem to have a somewhat more than hemispherical form, and exhibit on 
cross section as many as sixteen cells round the margin. These chambers are 
in direct communication with the finer branches of the ordinary canal system, 
which exhibits what is usually termed the fourth degree of complexity. An 
inner flattened nucleated epithelium could be detected as the lining of some of 
the canals. The afferent and efferent canals lie side by side, their parietal pores 
are adjacent, and beyond the distribution of the chambers and the direction of 
the increase in the diameter of the branch canals, I could detect no difference 
between them, and no special oscular or efferent regions. 

The Connective Tissue. — The mesodermic connective tissue exhibits great 
variety of composition in different regions. The cells vary greatly in shape, 
from round and regular to polygonal and multipolar, or to long drawn out 
spindle-like forms. Fine connecting threads between adjacent cells could be 
readily recognised. In some cases, besides nucleus and nucleolus, the intra- 



STRUCTURE OE SUBERITES DOMUECULA. 243 

cellular protoplasmic network could be distinctly seen. The great interest of 
the connective tissue, however, is its frequent modification into what may be 
termed muscle-cells. Disposed in compact strands, specially abundant in certain 
positions, these extended spindle-shaped cells certainly suggest a contractile 
function. A thick layer occurs just below the ectoderm; numerous well- 
defined, occasionally branching, strands run parallel to the surface somewhat 
further inwards ; a similar compactness of disposition is very abundant 
in the region adjoining the gasteropod shell, and lastly these muscle-strands 
frequently occur round the larger canalicular passages. While the strands 
of closely-packed spindle-shaped cells are quite definitely distinguishable, 
evident transitions exist between the latter and ordinary connective tissue 
cells (figs. 5-8). 

Reproductive Elements. — Embedded in the connective tissue matrix, I have 
observed the occurrence of developing sperms in the form of morula-like balls 
of minute cells, surrounded by an envelope of flattened connective tissue (fig. 
11). These balls of cells correspond with the sperm-morulae described by 
Schulze and Polejaeff. As ova occur in the same specimen, Suberites appears 
to be hermaphrodite. The ova occur, frequently in extraordinary abundance, 
throughout the whole sponge. In some cases two nuclei were present in the 
ovum, or a nucleus with a stained aggregate at each pole, — probably the 
beginnings of division. The chromatic contents of the germinal vesicle 
exhibited a most varied appearance, which seems to me worthy of special 
notice. Not one nucleolus, but several apparent nucleoli, were very generally 
present ; a smaller spherule often seemed to arise as a bud from the larger, or 
to lie adjacent to, though unconnected with it ; but more frequently three, 
four, or five variously disposed nucleolid spheres of perfectly definite contour, 
and uniformly stained, occurred. They were sometimes of equal size, but 
oftener with one slightly larger than the others. An idea of the varied 
disposition can be best obtained by a glance at a few nuclei represented in 
fig. 10. My friend Dr Heider has observed a horse-shoe-shaped nucleolus 
in sponge-ova, which might of course in cross section explain some of the 
forms. A more complex form might obviously show several spheres on 
cross section, and that this is the explanation is suggested by the nuclear sec- 
tions in fig. 10, several of which were cut through the same nucleus at different 
levels. It is also possible that we have here to deal with phenomena 
resulting, not from the complicated shape of the nucleolus, but from the 
occurrence of that multinucleolar condition which has, of late years, been 
repeatedly observed. 

As Suberites is but ill-suited for minute histological study, which could in 
such a form at most result in the confirmation of what can be better observed 
in other types, I have contented myself with attempting to elucidate the general 



244 MR J. ARTHUR THOMSON ON THE 

structure, and thus doing something towards increasing our knowledge of the 
almost unattached Monaxonia. 



Part II. 

Appended Note on the Capsules found on the surface of Spongelia pallescens. 

(Plate XVII.) 

In the course of some studies on sponges, pursued in the laboratory of the 
Zoological Institute at Berlin, Professor F. E. Schulze directed my attention 
to certain peculiar club-shaped knobs which were formed on the surface of a 
Spongelia, and entrusted them to me for examination. The death of the 
Spongelia prevented me from tracing their further history, and I can therefore 
at present only note their interesting structure, in the hope that others who 
may haye observed these or similar structures may be able to explain their 
import. 

The knobs were of the size of a small pin's head, and were raised above the 
level of the already contracted sponge by stalks formed from projecting peaks 
of the horny skeletal framework. The shape of the knobs was oval or pear- 
shaped, and their contour was always perfectly defined. 

Treatment with silver nitrate readily revealed the interesting fact that the 
knobs were surrounded by a well-defined ectoderm composed of cells of varying 
shape and size (fig. 11). 

The contents of a teased-out knob seemed to consist of generally round 
cells (figs. 3, 6) of very varied size, and with distinct nuclei, while sections of 
stained knobs exhibited what appeared as a compact and intricate meshwork 
of fine filaments, the meshes of which were occupied by cells of varied size (figs. 
4, 7). Towards the margins, and especially towards the base of the knob, the 
apparent network was looser, and there especially it could be seen that the 
structure was that of incipient tissue with undifferentiated cells, or of connective 
tissue in which the matrix was apparently wrinkled, or in some way modified 
round the cells, following their contours and producing the appearance of a 
very intricate filamentous network. The cells round the boundary, directly 
below the epithelium, were often very regular. Below these and at the base of 
knob, certain larger round cells (fig. 6) occurred, though by no means confined 
to these portions. Between these and the irregular cells of the meshwork 
intermediate forms were obvious. In some knobs the cells were almost all 
rounded (fig. 10), as if not compressed to the same extent. In others, as was 
especially well seen at the base, where the cells were less abundant, they 
exhibited the greatest variability of form (fig. 8). 

As these knobs present perfect definiteness of structure, and are only in 
formal contact with the sponge, it seems possible that they may thus secure the 



STRUCTURE OF SUBERLTES DOMUNCULA. 245 

persistence of the organism in unfavourable environment, which can of course 
only be verified by following their history. They might therefore be termed 
regenerative capsules. Somewhat similar aggregations or contractions were 
observed to occur in Renter a, but in these I was not able to make out any 
definite structure. 

As a histological modification in response to a change in the environment, 
whether it be connected or not with securing the persistence of the endangered 
organism, the occurrence of these structures is perhaps worthy of record. 



Explanation of Plates. 
Plate XVI. — Suberites. 

Fig. 1. External appearance, showing pores. 

2. Large section, showing spicules, canals, and ova, 

3. Ectodermic epithelium. 

i. System of canals, showing ciliated chambers. 

5-6. Muscle-cells. 

7-8. Connective tissue cells of mesoderm. 

9. Ova. 

10. Germinal vesicles with nucleoli. 

11. Sperm-morula?. 



Plate XVII. — Capsules of Spongelia. 



Fig. 1. Capsules on surface of sponge. 

2. Individual capsule on peak of sponge. 

3. Contents of capsule squeezed out. 

4. Longitudinal section. 

5. Border of capsule. 

6. Abundant round cells. 

7. Longitudinal section. 

8. Contained elements. 

9. Cross section. 

10. Longitudinal section with abundant round cells. 

11. Ectoderm outlines. 



VOL. XXXIII. PART. I. 2M 



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( 247 ) 



XI. — The Reproductive Organs of Bdellostoma, and a Teleostean Ovum 
from the West Coast of Africa. By J. T. Cunningham, B.A. 

(Read 5th July 1886.) 

During a short visit I paid to Oxford in the month of June last I had the 
opportunity of examining, by the kind permission of Professor Moseley, a 
number of specimens of Bdellostoma Forsteri, which were some of a large 
number brought from the Cape by Mr Adam Sedgwick of Trinity College, 
Cambridge. This examination showed what, from the close affinity of the two 
forms, was naturally to be expected, namely, that the structure of the repro- 
ductive system and the development of the reproductive elements in Bdel- 
lostoma were very closely similar to the structure and development of the 
corresponding parts in Myxine. A short time ago I described before the 
Society some ovarian eggs of Myxine, obtained at the beginning of the present 
year, which were approaching maturity. In these eggs there were slight pro- 
jections at the poles, and on the surface of the projecting parts a number of 
papillae. The projections were caused by the growth of a number of threads 
from the vitelline membrane within the ovarian capsule, and the papillae were 
the separate elevations produced by the threads. In one of the specimens of 
Bdellostoma which I examined at Oxford there were a number of ovarian eggs 
in an exactly similar condition. These eggs of Bdellostoma are of course much 
larger than those of Myxine ; the eggs of the latter, in the condition I refer to, 
were 21 cm., those of the former are 35 cm. No one has seen the perfectly 
ripe eggs of Bdellostoma after their escape from the ovary, but the specimens 
I have described prove conclusively that the eggs of this species when shed are 
provided with a number of polar threads, which are processes of the vitelline 
membrane, exactly as in Myxine. I have not yet made a microscopic 
examination of the reproductive organs in Bdellostoma, but from what I could 
see by ordinary dissection, it is evident that all the peculiarities which exist in 
the reproductive system in Myxine occur also in Bdellostoma. A number of 
specimens possessed sexual organs, in the anterior part of which were minute 
ova, while the posterior part was evidently testicular tissue; and in one or two 
other specimens the whole organ seemed to be testicular. The small quantity 
of testicular tissue in a given specimen was also noticeable, as in Myxine. I 
found no specimens which showed indications of having recently discharged 
their eggs. I have ascertained from Mr Sedgwick that his specimens were 
collected in August and September, and this fact shows that the breeding period 

VOL. XXXIII. PART T. 2 N 



248 MR J. T. CUNNINGHAM ON THE REPRODUCTIVE ORGANS 

of Bdellostoma agrees with that of Myxine in falling within the coldest season 
of the year. Myjcine glutinosa, in the North Sea, deposits its eggs in December, 
January, and February, and the two latter months agree in meteorological 
conditions with the months of August and September in the latitude of Cape 
Town. 

The egg of Bdellostoma at the stage under consideration has a thicker and 
stronger vitelline membrane than the egg of Myxine. I found it impossible to 
strip off from preserved specimens of the latter the connective tissue and 
follicular epithelium without rupturing the vitelline membrane. In the eggs of 
Bdellostoma this could be accomplished with ease. The membrane, when 
exposed, was seen to be yellowish-brown in colour, and translucent. Round 
the micropylar end of the capsule formed by the membrane is seen a distinct 
thin line, forming a complete ring, and it is evident that the micropylar 
end forms an operculum which separates from the rest of the capsule 
along this line. Steenstrup has figured a detached operculum in the figure 
he gives of the ova of Myxine, but in the latter form I have not yet detected 
indications of the structure. There can be no doubt, from the appear- 
ance seen in the Bdellostoma ovum, that the escape of the embryo in the 
Myxinoids is effected by the removal of an operculum specially adapted for 
that purpose. 

The Teleostean ova I have next to describe resemble in the character of the 
vitelline membrane the ova of the Myxinoids. Each ovum is spherical in 
shape, 1*5 to 1*6 mm. in diameter, and about one pole of the sphere is pro- 
vided with a number of long thin flexible filaments springing from the vitelline 
membrane. Each filament commences at the attached base with a conical 
papilla, which is thicker than the filament itself. By the interlacing of the 
filaments a large number, many thousands, of eggs are connected together 
to form a cylindrical mass about an inch wide, and a foot or more in length. 
The felted filaments form a rope-like core to the cylinder, the eggs forming 
an external layer. Besides the long filaments, each egg shows a similar 
number of short filaments springing from the opposite pole. These are very 
slender, and only from 2 mm. to 15 cm. in length. In other respects they 
resemble the long filaments, of which they are evidently rudimentary repre- 
sentatives. They seem to have no function, being too small to afford any 
assistance in the process of attachment. It is probable, though I have not 
been yet able to demonstrate the fact, that the micropyle is situated in the 
centre of the region whence the long filaments arise. If this were so, the rela- 
tions of the filaments and vitelline membrane in this Teleostean egg would be 
exactly similar to those which obtain in the ovum of the Myxinoids. And 
whatever be the position of the micropyle, it is interesting to note that the 
occurrence of a group of filamentous processes of the vitelline membrane at each 



OF BDELLOSTOMA AND A TELEOSTEAN OVUM. 249 

of the two opposite poles of the ovum is not peculiar to the Myxinoicls. It is 
as certain as an inference from the unfertilised ovum can be, that the 
segmentation of the egg of the Myxinoids is meroblastic, as in Teleosteans, and 
thus in two points the Myxinoid ovum agrees with the Teleostean, and differs 
from that of Petromyzon, while in respect of the mass of the yolk the 
Myxinoids agree more with Elasmobranchs. 

I have not succeeded in identifying the species of fish to which belong the 
eggs above described. The eggs of several species are known to be provided 
with filamentous processes. In the Scombresociclae the filaments are equal in 
length to the diameter of the ovum, and are uniformly distributed over the 
surface of the membrane. The filaments in this family were first described by 
Professor Haeckel.* John A. Eyder gives a very clear and complete account 
of them in the Bulletin of the U. S. Fish Commission, 1881, vol. L, as studied in 
Belone longirostris. In Chirostoma, one of the Atheriniclae, Ryder found 
there were only four filaments attached at one pole of the egg close together. 
In this latter case the filaments were during development closely wound 
round the vitelline membrane in one equator of the sphere, so that the 
method of their formation differs from that of the Myxinoid filaments, which 
are perpendicular to the surface of the membrane throughout their growth in 
the follicle. 

Filamentous processes of the vitelline membrane occur also in the family 
Pomacentridae ; they have been described by Hoffmann in Heliastes chromis 
of the Mediterranean (see Konink. Akad. d. Vetensk. Amst., vol. xxi.). Here 
they occur at one end only of the ellipsoidal ovum. They occur also in 
Gobius and Blennius, but in neither of these cases are two sets of processes 
present, situated at opposite poles of the ovum. It is thus impossible to say 
whether the ova described in this paper belong to a fish of the family 
Scombresocidae among the Physostomi, of the family Pomacentridae, or coral- 
fishes among the Pharyngognathi, of the family Gobiidae, Blennidae or 
Atherinidae, or to a species of some other family whose eggs are alto- 
gether unknown. The ova were obtained on two occasions, each time a 
single cylindrical "rope," by Mr John Rattray, F.R.S.E., in the Gulf of 
Guinea. Mr Rattray was on board a steamer called the "Buccaneer" last 
winter, in the capacity of naturalist, having been invited to accompany Mr J. 
Y. Buchanan, who was carrying out some hydrographical investigations off the 
coast of Africa. The eggs were obtained in the following manner : — A small 
conical buoy was attached at the end of a rope, and along the rope were 
fastened two or three muslin tow-nets. The whole was then thrown overboard 
in such a way that the mouth of the tow-net faced whatever current was flow- 
ing. The eggs were found entangled on the line when the apparatus was 

* Muller's Archiv, 1855. 



250 THE REPRODUCTIVE ORGANS OF BDELLOSTOMA, ETC. 

recovered. On the first occasion, March 12th of the current year, the position 
was lat. 1° 17' N., long. 13° 56 /# 6 W. The depth at which the ova were caught 
by the line was 30 fathoms. The total depth of the ocean at the spot was 
2725 fathoms. The other mass of eggs was taken in a similar way, not far off 
the locality just defined. Thus these eggs were in a pelagic condition, suspended 
in the water, and freely obeying the ocean current. Mr Rattray states they 
were very transparent. 

P.S. — Since the above was written I have found that the meroblastic 
nature of the ovum of Myxine has been actually proved. Fertilised eggs, in 
which the blastoderm had already begun to spread over the yolk, were examined 
and described by W. Muller several years ago (Jenaiscke Zeitschrift, Bel. IX.). 
These eggs were from the collection of the Goteborg Museum, and were 
obtained at Lysekil in Bohuslan in 1854. W. Muller, however, did not give 
a correct account of the development of the vitelline membrane and polar 
threads. 



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26 JUU 186? 




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16 



r-KIMKIi l!Y REILL AND COMPANY, ED1NUUKU1I. 



11 v. ■ ■* 1888 



TRANSACTIONS 



OF Tin: 



IOYAL SOCIETY OF EDINBURGH. 

VOL. XXXIII. PART II.— FOR THE SESSION 1886-87. 




CONTENTS. 



ST. XII. 

XIII. 

XIV. 
XV. 

XVI. 
XVII. 

XVIII. 
XIX. 

XX. 



XXI. 

XXII. 
XXIII. 

XXIV 

XXV. 



Page 

On the Foundations of the Kinetic- Theory of Oases. II. By Professor Tait, . 251 

Tables for Facilitating the Computation of Differential Refraction in Position 

Angle and Distance. By the Hon. Lord M'Laren, . . 279 

On a Class of Alternating Function*. By Thomas Muir, LL.D., . . 309 

Expansion if Functions in terms of Linear, C'y/indric, Spherical, and Allied 

Functions. By P. Alexandkk, M.A. Communicated by Dr T. Mum, . 313 

On Cases of Instability in Open Structures. By E. Sang, LL.D., . . 321 

On the Fossil Flora of the Radstoek Series of /he Somerset and Bristol Coal 
Field (Upper Coal Measures). Parts I., II. By Robert Kidston, F.K.S.E., 
F.G.S. (Plates XVIII.-XXVIIL), ..... 335 

A Diatomaceous Deposit from North Tolsta, Lewis. By John Rattray, M.A., 

B.Sc, of H.M. "Challenger" Commission, Edinburgh. (Plate XXIX.), . 419 

On the Minute Structure of the Eye in certain Cymothoidte. By Frank E. 
Beddard, M.A., F.R.S.E., FZ.S., Prosector to the Zoological Society, and 
Lecturer on Biology at Guy's Hospital. (Plate XXX.), . . . 443 

Report on the Pennatulidn dredged by H.M.S. "Porcupine!' By A. Milnes 
Marshall, M.D., D.Sc, M.A., F.R.S., Beyer Professor of Zoology in the 
Owens College ; and G. H. Fowler, B.A., Ph.D., Berkeley Fellow of the 
Owens College, Manchester. Communicated by John Murray, Esq. 
(Plates XXXI., XXXIL), ....... 453 

On the Determination of the Curve, on one if the coordinate planes, which forms 
the Outer Limit of the Positions of the point of contact of an Ellipsoid which 
always touches the three planes of reference. By G. Plarr, Docteur es- 
sciences. Communicated by Professor Tait, .... 465 

On the Partition of Energy between the Translator y and Rotational Motions of 

a Set of Non-Homogeneous Elastic Spheres. By Professor W. Burnside, . 501 

A Contribution la our Knowledge of the Physical Properties of Methyl-Alcohol. 
By W. Dittmar, F.R.SS. Lond. & Edin., and Charles A. Fawsitt. 
(Plate XXXIIL), ........ 509 

On the Thermal Conductivity of Iron, Copjper, and German Silver. By A. 
Criohton Mitchell, Esq. Communicated, with an Introduction, by Pro- 
fessor Tait. (Plates XXXIV, XXXV), ..... 535 

Critical Experiments on the Chloroplatinate Method for the Determination of 
Potassium, Rubidium, and Ammonium; and a Redetermination of the 
Atomic Weight of Platinum. By W. Dittmar and John M'Arthur, . 561 



[Issued April 13, 1888.} 



( - ? 51 ) 



XII. — On the Foundations of the Kinetic Theory of Gases. II. 

By Professor Tait. 

(Read December 6, 1S86, and January 7, 1887. Revised April 4, 1887.) 



PAGE 

Introductory and Preliminary, . . 251 

Part X. On the Definite Integrals, j vV r 

J T 

and J^. 2 ' §§33,34, . 256 



INDEX TO CONTENTS. 

PACE 



Part XI. Pressure in a Mixture of Two 

Sets of Spheres, § 35, . . 258 
„ XII. Viscosity, §§ 36, 37, . . 259 
„ XIII. Thermal Conductivity, §§38-44, 261 
„ XIV. Diffusion, §§ 45-56, . .266 

Appendix. Table of Quadratures, . .277 



[Erratum in Part I., ante, p. 65. For 1676, read 1678, as the date of Hooke's Pamphlet.] 



In the present communication I have applied the results of my first paper 
to the question of the transference of momentum, of energy, and of matter, in 
a gas or gaseous mixture ; still, however, on the hypothesis of hard spherical 
particles, exerting no mutual forces except those of impact. The conclusions 
of §§ 23, 24 of that paper form the indispensable preliminary to the majority of 
the following investigations. For, except in extreme cases, in which the causes 
tending to disturb the " special " state are at least nearly as rapid and persistent 
in their action as is the process of recovery, we are entitled to assume, from 
the result of § 24, that in every part of a gas or gaseous mixture a local special 
state is maintained. And it is to be observed that this may be accompanied 
by a common translatory motion of the particles (or of each separate class of 
particles) in that region ; a motion which, at each instant, may vary continuously 
in rate and direction from region to region; and which, in any one region, may 
vary continuously with time. This is a sort of generalisation of the special 
state, and all that follows is based on the assumption that such is the most 
general kind of motion which the parts of the system can have, at least in any 
of the questions here treated. Of course this translational speed is not the 
same for all particles in any small part of the system. It is merely an average, 
which is maintained in the same roughly approximate manner as is the 

VOL. XXXIII. PART II. 2 



252 PROFESSOR TAIT ON THE 

" special state," and can like it be assumed to hold with sufficient accuracy to 
be made the basis of calculation. The mere fact that a "steady" state, say of 
diffusion, can be realized experimentally is a sufficient warrant for this assump- 
tion ; and there seems to be no reason for supposing that the irregularities of 
distribution of the translatory velocity among the particles of a group should be 
more serious for the higher than for the lower speeds, or vice versa. For each 
particle is sometimes a quick, sometimes a slow, moving one : — and exchanges 
these states many thousand times per second. All that is really required by 
considerations of this kind is allowed for by our way of looking at the mean 
free paths for different speeds. 

I may take this opportunity of answering an objection which has been 
raised in correspondence by Professor Newcomb, and by Messrs Watson and 
Burbury, to a passage in § 3 of the First Part of this paper.* The words 
objected to are put in Italics : — 

"But the argument above shows, further, that this density must be ex- 
pressible in the form 

whatever rectangular axes be chosen, passing through the origin." 

The statement itself is not objected to, but it is alleged that it does not 
follow from the premises assumed. 

This part of my paper was introduced when I revised it for press, some 
months after it was read ; the date of revision, not of reading, being put at the 
head. It was written mainly for the purpose of stringing together what had 
been a set of detached fragments, and was in consequence not so fully detailed 
as they were. I made some general statements as to the complete verification 
of these preliminary propositions which was to be obtained from the more 
complex investigations to which they led ; thus showing that I attached com- 
paratively little weight to such introductory matters. If necessary, a detailed 
proof can be given on the lines of § 21 of the paper. The " argument " in 
question, however, may be given as below. It is really involved in the 
italicised words of the following passage of § 1 : — " in place of the hopeless 
question of the behaviour of innumerable absolutely isolated individuals, the 
comparatively simple statistical question of the average behaviour of the various 
groups of a community." 

Suppose two ideal planes, parallel to x = 0, to move with common speed, x, 
through the gas. The portion of gas between them will consist of two quite 
distinct classes of particles : — the greatly more numerous class being mere 

* In the Phil. May., for April 1887, the same objection is raised by Prof. Boltzmann ; who has 
appended it to the English translation of his paper presently to be referred to. But he goes farther 
than the other objectors, and accuses me of reasoning in a circle. 



FOUNDATIONS OF THE KINETIC THEOEY OF GASES. 253 

fleeting occupants, the minority being (relatively) as it were permanent lodgers, 
These are those whose speed perpendicular to the planes is very nearly that of 
the planes themselves. The individuals of each class are perpetually changing, 
those of the majority with extraordinary rapidity compared with those of the 
minority; but each elms, as such, forms a definite "group of the community." 
The method of averages obviously applies to each of these classes separately ; 
and it shows that the minority will behave, so far as y and z motions are 
concerned, as if they alone had been enclosed between two material planes, 
and as if their lines of centres at impact were always parallel to these. The 
instant that this ceases to be true of any one of them, that one ceases to belong 
to the group ; — and another takes its place. Their behaviour under these 
circumstances (though not their number) must obviously be independent of the 
speed of the planes. Hence the law of distribution of components in the 
velocity space-diagram must be of the form 

and symmetry at once gives the result above. 

[[Inserted March 5th, 1887.) Another objection, but of a diametrically 
opposite character, raised by Mr Burbury " ;: " and supported by Professor 
Boltzmann, t is to the effect that in my first paper I have unduly multiplied 
the number of preliminary assumptions necessary for the proof of Maxwell's 
Theorem concerning the distribution of energy in a mixture of two gases. 
In form, perhaps, I may inadvertently have done so, but certainly not in 
substance. 

The assumptions which (in addition to that made at the commencement of 
the paper (§ 5) for provision against simultaneous impacts of three or more 
particles, which was introduced expressly for the purpose of making the results 
applicable to real gases, not merely to imaginary hard spheres,) I found it 
necessary to make, are (§ 18) as follows ; briefly stated. 

(A) That the particles of the two systems are thoroughly mixed. 

* The Foundations of the Kinetic Theory of Gases. Phil. Mag. 1886, I, p. 481. 

f Uber die zum theoretischen Beweise des Avogadro'-schen Gesetzes erforderlichen Voraussetzungen. 
Sitzb. derkais. Akad. XCIV, 1886, Oct. 7. In this article Prof. Boltzmann states that I have nowhere 
expressly pointed out that my results are applicable only to the case of hard spheres. I might plead 
that the article he refers to is a brief Abstract only of my paper ; but it contains the following state- 
ments, which are surely explicit enough as to the object I had in view : — 

" This is specially the case with his [Maxwell's] investigation of the law of ultimate partition of 
energy in a mixture of smooth spherical particles of two different kinds." 

" It has since been extended by Boltzmann and others to cases in which the particles are no longer 
supposed to be hard smooth spheres." 

"Hence it is desirable that Maxwell's proof of his fundamental Theorem should be critically 
examined." Then I proceed to examine it, not Professor Boltzmann's extension of it. In my paper 
itself this limitation is most expressly insisted on. 



254 PROFESSOR TAIT ON THE 

(B) That the particles of each kind, separately, acquire and maintain th.> 
" special state." 

(C) That there is free access for collision between each pair of particles, 
whether of the same or of different systems ; and that the number of particles 
of one kind is not overwhelmingly greater than that of the other. 

Of these, (A) and (B), though enunciated separately, are regarded as conse- 
quences of (C), which is thus my sole assumption for the proof of Clerk- 
Maxwell's Theorem. Professor Boltzmann states that the only necessary 
assumptions are : — that the particles of each kind be uniformly distributed in 
space, that they behave on the average alike in respect of all directions, and 
that (for any one particle X) the duration of an impact is short compared with 
the interval between two impacts. His words are as follows : — " Die einzigen 
Voraussetzungen sind, dass sowohl die Molekule erster als auch die zweiter 
Gattung gleichformig im ganzen Raume vertheilt sind, sich durchschnittlich 
nach alien Richtungen gleich verhalten und dass die Dauer eines Zusam- 
menstosses kurz ist gegen die Zeit, welche zwischen zwei Zusammenstossen 
vergeht. " 

He farther states that neither system need have internal impacts ; and that 
Mr Burbury is correct in maintaining that a system of particles, which are 
so small that they practically do not collide with one another, will ultimately 
be thrown into the " special " state by the presence of a single particle with 
which they can collide. 

Assuming the usual data as to the number of particles in a cubic inch of 
air, and the number of collisions per particle per second, it is easy to show 
(by the help of Laplace's remarkable expression * for the value of A "O m jn"' 
when m and n are very large numbers) that somewhere about 40,000 years 
must elapse before it would be so much as even betting that Mr Burbury's 
single particle (taken to have twice the diameter of a particle of air) had 
encountered, once at least, each of the 3.10 20 very minute particles in a single 
cubic inch. He has not stated what is the average number of collisions neces- 
sary for each of the minute particles, before it can be knocked into its destined 
phase of the special state ; but it must be at least considerable. Hence, even 
were the proposition true, aeons would be required to bring about the result. 
As a result, it would be very interesting; but it would certainly be of no 
importance to the kinetic theory of gases in its practical applications. 

I think it will be allowed that Professor Boltzmann's assumptions, which 
(it is easy to see) practically beg the whole question, are themselves inadmissible 

* Thiorie Analytique dee Probability. Lime II, rha/i. ii, 4. [In using this formula, we must 
make sure that the ratio m/n is sufficiently large to justify the approximation on which it is founded. 
It is found to be so in the present case. At my request Professor Cayley has kindly investigated the 
correct formula for the case in which m and n are of the same order of large quantities. His paper will 
be found in Proc R. S. K, April 4, 1887.] 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 255 

except (is consequences of the mutual impacts of the particles in each of the two 
systems separately. Professor Boltzmann himself, indirectly and without any 
justification (such as I have at least attempted to give), assumes almost all that 
he objects to as redundant in my assumptions, with a good deal more besides. 
But he says nothing as to the relative numbers of the two kinds of particles. 
Thus I need not, as yet, take up the question of the validity of Professor 
Boltzmann's method of investigation (though, as hinted in § 31 of my first 
paper, I intend eventually to do so) ; and this for the simple reason that, in 
the present case, I cannot admit his premises. 

Mr Burbuky assumes the non-colliding particles to be in the "special 
state," and proceeds to prove that the single additional particle will not disturb 
it. But, supposing for a moment this to be true, it does not prove that the 
solitary particle would (even after the lapse of ages) reduce any non-colliding 
system, with positions at any instant, speeds, and lines of motion, distributed 
absolutely at random (for here there cannot be so much as plausible grounds 
for the introduction of Professor Boltzmann's assumptions) to the " special 
state." If it could do so, the perfect reversibility of the motions, practically 
limited in this case to the reversal of the motion of the single particle alone, 
shows that the single particle would (for untold ages) continue to throw a 
system of non-colliding particles further and further out of the " special" state; 
thus expressly contradicting the previous proposition. In this consequence of 
reversal we see the reason for postulating a very great number of particles of 
each kind. If Mr Burbury's sole particle possessed the extraordinary powers 
attributed to it, it would (except under circumstances of the most exact adjust- 
ment) not only be capable of producing, but would produce, absolute confusion 
among non-colliding particles already in the special state. Considering what 
is said above, I do not yet see any reason to doubt that the assumption of 
collisions among the particles of each kind, separately, is quite as essential to 
a valid proof of Maxwell's Theorem as is that of collisions between any two 
particles, one from each system. I have not yet seen any attempt to prove 
that two sets of particles, which have no internal collisions, will by their 
mutual collisions tend to the state assumed by Professor Boltzmann. Nor can 
I see any ground for dispensing with my farther assumption that the number 
of particles of one kind must not be overwhelmingly greater than that of the 
other. A small minority of one kind must (on any admissible assumption) 
have an average energy which will fluctuate, sometimes quickly sometimes very 
slowly, within very wide and constantly varying limits. 

De Morgan* made an extremely important remark, which is thoroughly 
applicable to many investigations connected with the present question. It is 
to the effect that "no primary considerations connected with the subject of 

* Ennjc. Metropolitana. Art. Theory of Probabilities. 



250 PROFESSOR TAIT ON THE 

Probability can be, or ought to be, received if they depend upon the results of 
a complicated mathematical analysis." To this may be added the obvious 
remark, that the purely mathematical part of an investigation, however elegant 
and powerful it may be, is of no value whatever in physics unless it be based 
upon admissible assumptions. In many of the investigations, connected with 
the present subject, alike by British and by foreign authors, the above remark 
of De Morgan has certainly met with scant attention.] 

In my first paper I spoke of the errors in the treatment of this subject 
which have been introduced by the taking of means before the expressions were 
ripe for such a process. In the present paper I have endeavoured throughout 
to keep this danger in view ; and I hope that the results now to be given will be 
found, even where they are most imperfect, at least more approximately accurate 
than those which have been obtained with the neglect of such precautions. 

The nature of Clerk-Maxwell's earlier investigations on the Kinetic 
theory, in which this precaution is often neglected, still gives them a peculiar 
value ; as it is at once obvious, from the forms of some of his results, that he 
must have thought them out before endeavouring to obtain them, or even to 
express them, by analysis. One most notable example of this is to be seen in 
his Lemma {Phil. Mag. 1860, II. p. 23) to the effect that 



/ 



m + Z ax\ / 



where U and r are functions of x, not vanishing with x, and varying but slightly 
between the limits — r and r of x; — and where the signs in the integrand 
depend upon the character of m as an even or odd integer. This forms the 
starting point of his investigations in Diffusion and Conductivity. It is clear 
from the context why this curious proposition was introduced, but its accu- 
racy, and even its exact meaning, seem doubtful. 

In all the more important questions now to be treated, the mean free path 
of a particle plays a prominent part, and integrals involving the quantities e, or 
e + e l (as defined in §§9, 10, 28) occur throughout. We commence, therefore, 
with such a brief discussion of them as will serve to remove this merely 
numerical complication from the properly physical part of the reasoning. 

X. On the Definite Integrals 

/ V JL and 
Jo e 

33. In the following investigations I employ, throughout, the definition 
of the mean free path for each speed as given in § 11. Thus all my results 




FOUNDATIONS OF THE KINETIC THEORY OF GASES. 257 

necessarily differ, at least slightly, from those obtained by any other inves- 
tigator. 

By § 11 we see at once that 



/ vv r 1 / £ v av 

1 r 4x'- +i e-**dx 



(vv 1 /3+v 1 3 /v)dv 1 






s^-, suppose. 



The finding of C r is of course a matter of quadratures, as in the Appendix 
to the First Part of this paper, where the values calculated are, in this notation, 
d and C ; and Mr Clark has again kindly assisted me by computing the 
values of C x , C 3 , C 5 , which are those required when we are dealing with 
Viscosity and with Heat-Conduction in a single gas. The value of C 2 has also 
been found, with a view to the study of the general expression for C r . These 
will be given in an Appendix to the present paper. 

34. When we come to deal with Diffusion, except in the special case of 
equality of density in the gases, this numerical part of the work becomes 
extremely serious, even when the assumption of a " steady " state is permissible. 
As will be seen in § 28 of my first paper, we should have in general to deal 
with tables of double entry, for the expressions to be tabulated are of the 
form — 

/■» *r _j /*» 4s r+4 r* 3 <fa 

For the second gas the corresponding quantity will be written as 2 € r . Here 

Ws + sA 2 . 

IV2T) ' 



and 



nh. 



so that they are numerical quantities, of which the first depends on the relative 
masses of particles of the two gases, while the second involves, in addition, not 
only their relative size but also their relative number. It is this last condition 
which introduces the real difficulty of the question, for we have to express the 



258 PROFESSOR TAIT ON THE 

value of the integral as a function of z before we can proceed with the further 
details of the solution, and then the equation for Diffusion ceases to resemble 
that of Fourier for Heat- Conduction. 

The difficulty, however, disappears entirely when we confine ourselves to 
the study of the " steady state " (and is likewise much diminished in the study of 
a variable state) in the special case when the mass of a particle is the same in 
each of the two gaseous systems, whether the diameters be equal or no. For, 
in that case, we have h x = h and oc x = x, so that the factor 1/(1 + z) can be taken 
outside the integral sign. Thus, instead of x <& r , we have only to calculate C,. of 
the previous section. 



XI. Pressure in a Mixture of Two Sets of Spheres. 

35. Suppose there be n x spheres of diameter s x and mass P l5 and n % with 
s. 2) P 2 , per cubic unit. Let s = (s 1 + s 2 )/2. 

Then the average number of collisions of each P x with P x s is, per second, 

The impulse is, on the average (as in § 30), 

Similarly, each P x encounters, in each second (§ 23), the average number 

Mh t +h 2 ) g 

Z W h x i h s 

of P 2 s, and the average impact is 

p^py j h h 2 

Thus the average sum of impacts on a Pj is, per second, 



7T 

— 2P 1 ;-w l s 1 2 , due to PjS; and 

- 2 i(+p 2 ^7 7r ^ 2 ' duetoP ^- 

In the Virial expression <j2(Kr), {§ 30}, r must be taken as *, for the first of 
these portions, and as s for the second. Hence we have 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 259 

Y/"FM — — '"" / !« 2 « 3 4- Q 12^ 1 "*" ^L w o3 _i_ £_?», 2, 3 1 



= — -p{n i % 3 + 2n 1 n 2 !? + n. 2 \ 3 }; 



for Pi = P 2 = Pi+P2_l (^+'>A\JP > 

1\ h 2 h x + h 2 n\ h l h 2 ) n ' 

where 

n = n 1 + n 2 . 

In the special case s 1 = s 2 = s, this becomes, as in § 30, 

vS(Itr) = — irpns 3 . 

To obtain an idea as to how the " ultimate volume," spoken of in that 
section, is affected by the difference of size of the particles, suppose n x = n 2 . 
The values of the above quantities are 

— t-^'{s 1 3 + 2s 3 +s 2 3 } and — irnps 3 ; 

so that (as we might have expected) disparity of size, with the same mean of 
diameters, increases the quantity in question. 
Thus, if 

s 1 : s : s 2 : : 1 : 2 : 3 , 

the ratio of the expressions above is 11 : 8. The utmost value it can have (when 
sjs 2 is infinite, or is evanescent) is 5 : 2. 

XII. Viscosity. 

36. Suppose the motion of the gas, as a whole, to be of the nature of a 
simple shear ; such that, relatively to the particles in the plane of yz, those in 
the plane x have a common speed 

V = Bx 

parallel to y. V, even when x is (say) a few inches, is supposed small compared 
with the speed of mean square. We have to determine the amount of 
momentum parallel to y which passes, per second, across unit area of the plane 
of yz. 

In the stratum between x and x + Sx there are, per second per unit surface, 
nvevhx collisions discharging particles with speed v to v + dv (distributed 
uniformly in all directions) combined, of course, with the speed of translation 
of the stratum. The number of these particles which cross the plane of yz at 
angles to 6 + dO with the axis of x is 

g-«* 8 ece s i n QdQ/2. 
VOL. XXXIII. PART II. 2 P 



260 PROFESSOR TAIT ON THE 

[Strictly speaking, the exponent should have had an additional term of the 
order eBa?/v ; but this is insensible compared with that retained until x is a 
very large multiple of the mean free path. See the remarks in § 39 below.] 
Each takes with it (besides its normal contribution, which need not be con- 
sidered) the abnormal momentum 

PBcc, 

relatively to yz and parallel to y. 

Hence the whole momentum so transferred from x positive is 



FBn 




vV / sin0rf0 / s - exsec9 exdx, 



or 




Doubling this, to get the full differential effect across the plane of yz, it becomes 
(§33) 

PBnC, PBra 0-838 

37T?is 2 Jh 3tt?is 2 Jh 

The multiplier of B, i.e. of dYjdx, is the coefficient of Viscosity. Its 
numerical value, in terms of density and mean path, is 

4:0-412. 

Jh 



Clerk-Maxwell, in 1860, gave the value 

-0-376 , 



PL 
Jh" 



which (because l = 707\/Q77, as in § 11) differs from this in the ratio 20 :21. In 
this case the short cuts employed have obviously entailed little numerical error. 
Since p\ is constant for any one gas, the Viscosity (as Maxwell pointed out) is 
independent of the density. 

37. Both expressions are proportional to the square-root of the absolute 
temperature. We may see at once that, on the hypothesis we have adopted, 
such must be the case. For, if we suppose the speed of every sphere to be 
suddenly increased m fold, the operations will go on precisely as before, only m 
times faster. But the absolute temperature will be increased as m 2 : 1. Similar 
anticipations may be made in the cases of Diffusion and of Thermal Conduc- 
tivity. 



FOUNDATIONS OF THE KINETIC THEORY OE GASES. 261 

Maxwell was led by his experimental measures of Viscosity, which seemed 
to show""' that it increases nearly in proportion to the first power of the absolute 
temperature, to discard the notion of hard spheres, and to introduce the 
hypothesis of particles repelling one another with force inversely as the fifth 
power of the distance. I have already stated that there are very grave ob- 
jections to the introduction of repulsion into this subject, except of course in 
the form of elastic restitution. That the particles of a gas have this property 
is plain from their capability of vibrating, so that they must lose energy of 
translation by impact ; and I intend, in the next instalment of this investigation, 
so far to modify the fundamental assumption hitherto made as to deduce the 
effects corresponding to a coefficient of restitution less than unity; and also to 
take account of molecular attraction, specially limited in its range to distances 
not much greater than the diameter of a sphere. 

XIII. Thermal Conductivity. 

38. We must content ourselves with the comparatively simple case of the 
steady flow of heat in one direction ; say parallel to the axis of x. This will be 
assumed to be vertical, the temperature in the gas increasing upwards, so as to 
prevent convection currents. No attention need, otherwise, be paid to the 
effects of gravity. 

Hence the following conditions must be satisfied : — 

(a) Each horizontal layer of the gas is in the special state, compounded 

with a definite translation vertically. 

(b) The pressure is constant throughout the gas. 

(c) There is, on the whole, no passage of gas across any horizontal plane. 

(d) Equal amounts of energy are, on the whole, transferred (in the same 

direction) across unit area of all such planes. 

39. Let n be the number of particles per unit volume in the layer between 
x and x + dx; v the fraction of them whose speed, relatively to the neighbours 
as a whole, lies between v and v + dv ; a the speed of translation of the layer. 

The number of particles which pass, per unit area per second, from x positive 
through the plane x = 0, is the sum of those escaping, after collision, from all the 
layers for positive, x, and not arrested on their way : — viz., 

\ f P /£«•—•/•""■ sin 6d6 vcos0 -^dx . 

?/o Jo Jo vcos6 

Here a, though in any ordinary case it need not be more than a very small 
fraction of an inch, is a quantity large compared with the mean free path of a 

* Cf., however, Stokes, Phil. Trans., 1886, vol. clxxvii. p. 786. 



262 PROFESSOR TAIT ON THE 

particle. Its value will be more exactly indicated when the reason for its 
introduction is pointed out. 

The last factor of the integrand depends on the fact that the particles are 
emitted from moving layers : — involving the so-called Doppler, properly the 
Komer, principle. 

We neglect, however, as insensible the difference between the absorption due 
to slowly moving layers and that due to the same when stationary. 

Because a, the range of x, is small we may write with sufficient approxima- 
tion 

n = n + n 'x, &c, &c. 

Introducing this notation, the expression above becomes 

2 Jo J o Jo °° °\ \% v e J J vcos0 

Now, to the degree of approximation adopted, 

/ edx = e x + e 'x 2 /2 . 
Jo 

The second term of this must always be very small in comparison with the 
first, even for an exceptionally long free path. But, if we were to make 

30 = -' e o/ e o 

the second term would become equal to the first. Hence a, the upper limit of 
the x integration, must be made much smaller than this quantity. Thus we 
may write 

g - sec O/'edx = 6 -e x sec 9(1 _ e^ggg 0/2 + . . . ) . 

We said, above, that 

/l 

CM = ah- 



lS a large number, say of the order 10 2 . It appears then at once that terms in 

g -, « =g -100 =1 0- 43 uear ly 

may be neglected. Such terms occur at the upper limit in the integration with 
regard to x above, and what we have said shows, first why a had to be intro- 
duced, second why it disappears from the result. 

Writing now only those factors of the above expression which are concerned 
in the integration with respect to x, we have 

/ (l + ( j' + V f + %f)x + . . . Vl - e 'xhee 8/2 + . . . V «>*»ec »dx , 
or 

l( C08 e+^(<+<) C0S w). 

e \ e \n V J ) 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 263 

The terms in e ' are found to have cancelled one another, a result which greatly 
simplifies the investigation. 

Had we complicated matters by introducing a + a ',z in place of a, the term 
in a ' (which, if it exist at all, is at least very small) would have been divided 
on integration twice by e , a quantity whose value is, on the average, of the 
order 5 . 10 5 (to an inch as unit of length). 

The expression now becomes 

T/yM^+T) 3 ^'"'-)** 9 - 

We have omitted the zero suffixes, as no longer required ; and, as the plane 
jc = is arbitrary, the expression is quite general. 

Omitting the product of the two small terms, and integrating with respect 
to 0, we have 

The corresponding expression for the number of particles which pass through 
the plane from the negative side is, of course, to be obtained by simply chang- 
ing the signs of the two last terms. Thus, by (c) of § 38, we have 



/i 



or 



H£4)*)=°< 



40. The pressure at the plane x = 0, taken as the whole momentum (parallel 
to jd) which crosses it per unit area per second, is to be found by introducing 
into our first integrand the additional factor 

P(w COS Q — ot), 

where P is the mass of a particle. There results 

V 3 — +S+7> 2 / 46 )- 



2" I nv\fl 



We must take the sum of this, and of the same with the signs of the two last 
terms changed ; so that the pressure (which is constant throughout, by (b) of 
§ 38) is 






■2h 
Thus n/h is constant throughout the gas. 



p r x Tn 

P = ~3 I nvv2== oT • ( 2 -) 



2(54 PROFESSOR TAIT ON THE 

[If a very small, thin, disc were placed in the gas, with its plane parallel 
to yz, and the steady state not thereby altered, the difference of pressures on its 
sides would be 



" p /" ; ( ! »-(l+7H 

J 



or 

For ordinary pressures, and a temperature gradient 10° C. per inch, this is of 
the order 10" 7 atmosphere only.] 

41. For the energy which passes per second per unit of area across cc = 0, 
we must introduce into the first integrand of § 39 the additional factor 

-^-(v 2 — 2vxcos0\ ; 

and the result of operations similar to those for the number of particles is 



*=-! 



-/•<(7 + v)/*W0 (3> 



This expresses the excess of the energy passing from the negative to the 
positive side of cc = 0, over that passing from positive to negative ; and, by (d) 
of § 38 must be constant. 

42. To put (1) and (3) in a more convenient and more easily intelligible 
form, note that because 



we have 
But, by (2), 

Thus, by (1), 



»/=4 Pt-^vHv 

v 3 h' 7/ „ 
v A II 

ri_ ll_ 
n h ' 



/5 C 1 -C 3 ) . . . (1'.) 



Similarly (3) becomes 



Jh b <6pirs \2 



E =jl-6^(¥ C '- OC = + C ' <« 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 265 

43. The only variable factor (tijlfi) in these expressions for a. and for E, is 
the same in both. Hence, as E does not vary with x, h'fhfc is constant, and so 
also is a. Thus since, if t be absolute temperature, we have 

lir = constant ; 

we find at once, 

T 1 = A + Bx. 

Thus the distribution of temperature, and therefore that of density, is deter- 
mined when the terminal conditions are given. The formula just given agrees 
with the result first obtained by Clausius in an extremely elaborate investiga- 
tion,* in which he showed that Maxwell's earliest theory of Heat-Conduction 
by gases is defective. 

The general nature of the motion of the gas is now seen to be analogous to 
that of liquid mud when a scavenger tries to sweep it into a heap. The broom 
produces a translatory motion of the mud, which is counteracted by gravita- 
tion-sliding due to the surface gradient : — just as the displacement (by trans- 
lation) of the whole gas, from hot to cold, is counteracted by the greater 
number of particles discharged (after collisions) from a colder and denser layer, 
than from an adjoining warmer and less dense layer. 

44. The results of calculation of values of C,. given in the Appendix enable 
us to put the expressions (!') and (3') into the more convenient forms 



a = 



h ' ^0-06 (!".) 



Jh b p 



E^-^AO-45 . . . . (3".) 

where it is to be remarked that the product p\ is independent of the tempera- 
ture of the gas. 

The Conductivity, k, is defined by the equation 

*£--■■ 

and thus its value is 

V T 3 VV 

where r , h are simultaneous values of r and k. 

At 0° C. (i.e. t = 274) this is, for air, nearly 3.10 ~ 5 in thermal units on 
the pound-foot-minute-Centigrade system : — i.e. about 1/28,000 of the con- 
ductivity of iron, or 1/3600 of that of lead.t Of course, with our assumption 

* Pogg. Ann., cxv, 1862 ; Phi!. Mag., 1862, I. 
f Trans. R. S. E., 1878, p. 717. 



266 PROFESSOR TAIT ON THE 

of bard spherical particles, we have not reckoned the part of the conducted 
energy which, in real gases, is due to rotation or to vibration of individual 
particles. 

XIV. Diffusion. 

45. The complete treatment of this subject presents difficulties of a very 
formidable kind, several of which will be apparent even in the comparatively 
simple case which is treated below. We take the case of a uniform vertical 
tube, of unit area in section, connecting two vessels originally filled with different 
gases, or (better) mixtures of the same two gases in different proportions, both, 
however, maintained at the same temperature ; and we confine ourselves to the 
investigation of the motion when it can be treated as approximately steady. 
We neglect the effect of gravity (the denser gas or mixture being the lower), 
and we suppose the speeds of the group-motions to be very small in compari- 
son with the speed of mean square in either gas. [In some of the investigations 
which follow, there are (small) parts of the diffusion-tube in which one of the 
gases is in a hopeless minority as regards the other. Though one of the initial 
postulates (d of § 1) is violated, I have not thought it necessary to suppress the 
calculations which are liable to this objection; for it is obvious that the condi- 
tions, under which alone it could arise, are unattainable in practice.] 

Clerk-Maxwell's Theorem (§ 15), taken in connection with our preliminary 
assumption, shows that at every part of the tube the number of spheres per 
cubic unit, and their average energy, are the same. Hence, if n v n 2 , be the 
numbers of the two kind of spheres, per cubic unit, at a section x of the tube 

oi 1 + n 2 = n = constant, (1.) 

Also, if P 1? P 2 , be the masses of the spheres in the two systems respectively, 
h x and h 2 the measures (§ 3) of their mean square speeds, we have 

PA = P 2 /fi 2 = KPA + n 2 TJh 2 )jn = 2 P /n, . . . (2.) 

where p is the constant pressure. 

Strictly speaking, the fact that there is a translational speed of each layer 
of particles must affect this expression, but only by terms of the first order of 
small quantities. 

46. The number of particles of the P x kind which pass, on the whole, 
towards positive x through the section of the tube is (as in § 39) 

/* CO 

where a, is the (common) translational speed of the P : s, and l/e 1 the mean 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 267 

free path of a P : whose speed is v. We obtain this by remarking that, in the 
present problem, h x is regarded as constant, so that there is no term in v{. 

Hence, if G x be the mass of the first gas on the negative side of the section, 
divided by the area of the section, we have 

^h=-F 1 (n 1 « 1 -r,; i € 1 l3) . . . . (3.) 

If G 2 be the corresponding mass of the second gas, we have (noting that, 
by (1), < + < = 0) 

^-P^V^+V.^/3) (4.) 

From the definitions of the quantities G l3 G 2 , we have also 

dG,_ v fW,_ p , >j 

~dx~ ~ 1% ' dx* " ^ ' I 

> ■ • ■ • (5.) 
dG,_ rf 2 G 2 _ p , | 

dx~ 1 ^' dx*-~^ n '- J 

47. We have now to form the equations of motion for the layers of the two 
gases contained in the section of the tube between x and x + Sx. The increase 
of momentum of the P x layer is due to the difference of pressures, behind and 
before, caused by P x s ; minus the resistance due to that portion of the impacts 
of some of the PjS against P 2 s in the section itself, which depends upon the 
relative speeds of the two systems, each as a whole. This is a small quantity 
of the order the whole pressure on the surfaces of the particles multiplied by 
the ratio of the speed of translation to that of mean square. The remaining 
portion (relatively very great) of the impacts in the section is employed, as we 
have seen, in maintaining or restoring the "special state" in each gas, as well 
as the Maxwell condition of partition of energy between the two gases. If R 
be the resistance in question, the equations of motion are 

a up t' ' ' (6 ' } 

where d represents total differentiation. 

48. To calculate the value of R, note that, in consequence of the assumed 
smallness of a 1} a 2 , relatively to the speeds of mean square of the particles, the 
number of collisions of a P x with a P 2 , and the circumstances of each, may be 
treated as practically the same as if a t and a 2 were each zero : — except in so far 

VOL. XXXIII. PART II. 2 Q 



268 PROFESSOR TAIT ON THE 

that there will be, in the expression for the relative speed in the direction of 
the line of centres at impact, an additional term 

(« x — a 2 )cos \Js , 

where xfj is the inclination of the line of centres to the axis of x. Thus to the 
impulse, whose expression is of the form 

2PQ , x 
(u-v), 



P+Q 



as in § 19 of the First Part of the paper, there must be added the term we seek, 
viz., 

~F^fP (ai_a2)cos ^' 

This must be resolved again parallel to x, for which we must multiply by 
cos \jj. Also, as the line of centres may have with equal probability all 
directions, we must multiply further by sin \jjd\jj/2, and integrate from to it. 
The result will be the average transmission, per collision, per P 1? of translatory 
momentum of the layer parallel to x. Taking account of the number of impacts 
of a Pj on a P 2 , as in § 23, we obtain finally 



p 4 /•n-iK + h) P i P 2 / \ n\ 

x-jnpf V-^- 1 p^p^-^ • • < 7 -> 



where s is the semi-sum of the diameters of a P x and a P 2 . 

49. To put this in a more convenient form, note that (2), in the notation of 

(5), gives us the relation 

Id&i 1 dG, 

h-y dx h 2 dx " ' 
whence 

G 1 /h, + G 2 /h, = 2px (8.) 

We have not added an arbitrary constant, for no origin has been specified 
for x. Nor have we added an arbitrary function of t, because (as will be seen 
at once from (3)) this could only be necessary in cases where the left-hand 
members of (6) are quantities comparable with the other terms in these equa- 
tions. They are, however, of the order of 

dt* dxdt Ul ' &C -' 

and cannot rise into importance except in the case of motions much more 
violent than those we are considering. 
From (8) we obtain 

f/*'+f/'«°=°- • <w 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 269 

which signifies that equal volumes of the two gases pass, in the same time, in 
opposite directions through each section of the tube. This gives a general 
description of the nature of the cases to which our investigations apply. 
But, by (3) and (4), we have for the value of 

PjPjn^o!— « 2 ) 
the expression 



or, by (9), (2), and (5) 



*(5-e2w^> 



Substituting this for the corresponding factors of R in the first of equations 
(6), and neglecting the left-hand side, we have finally 

°~ 2J h da? + 3 S V ] h i h P 1 + P 2 1 It 3» li x j( n -n®i + n i&i> j 
or 

dGi_( 3 p i + p 2 1,1, - , arMGti. 

~df~{l6? Mh+h)KK ' p + 3n> n ^ +7h ^ ) )dx 2 ' 

or, somewhat more elegantly, 

dG-, /3 /Jh+K-, I, ((r , -A^&i nn\ 

^- = (8^V iyif+S^x^+^A)]-^- ' • • (10,) 

50. This equation resembles that of Fourier for the linear motion of heat ; 
but, as already stated in § 34, the quantities (^ which occur in it render it in 
general intractable. The first part of what is usually called the diffusion- 
coefficAent (the multiplier of dPGJdot? above) is constant ; but the second, as is 
obvious from (5) and (8), is, except in the special case to which we proceed, a 
function of dQJdx ; i.e. of the percentage composition of the gaseous mixture. 

51. In the special case of equality, both of mass and of diameter, between 
the particles of the two systems, the diffusion-coefficient becomes 



D "8?is 2 V' 



2 , C, 



7rA 3»7TS 2 Jh ' 

or 

D _f3 /t , CA X X 

U ~ W 2 + 3 J 0-677 ,/A~ ^A ' 

where X is the mean free path in the system. Hence the diffusion- coefficient 
among equal particles is directly as the mean free path, and as the square root 
of the absolute temperature. Fourier's solutions of (10) are of course applic- 
able in this special case. 



270 PROFESSOR TAIT ON THE 

If we now suppose that our arrangement is a tube of length I and section S, 
connecting two infinite vessels filled with the two gases respectively; and, 
farther, assume that the diffusion has become steady, the equation (10) 
becomes 

dt dx 2, 

where the left-hand member is constant. Also, it is clear that, since dQJdx 
must thus be a linear function of x, we have 



S^-K 1 -?)' 



so that the mass of either gas which passes, per second, across any section of 
the tube is 

where p is the common density of the two gases. 

For comparison with the corresponding formulas in the other cases treated 
below, we may now write our result as 

Also, to justify our assumption as to the order of the translatory speed, we 

find by (3) 

1-38X 



\l-x)Jh 



Hence, except where l—x is of the order of one thousandth of an inch or less, 
this is very small compared with h~ l . And it may safely be taken as impossible 
that n x can (experimentally) be kept at at the section x = l. 

If the vessels be of finite size, and if we suppose the contents of each to be 
always thoroughly mixed, we can approximate to the law of mixture as follows. 
On looking back at the last result, we see that for p we must now substitute 
the difference of densities of the first gas at the ends of the connecting tube. 
Let g v g 2 be the quantities of the two gases which originally filled the vessels 
respectively ; and neglect, in comparison with them, the quantity of either gas 
which would fill the tube. Then, obviously, 



r/G 1= SDp/Gt fl-GA 
dt " I \f/ 1 g 2 J' 



whence 



G = -71.72 Hl + £ i 9l9t { 



This shows the steps by which the initial state (g lt 0) tends asymptotically to 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 271 

the final state ( }/ 9\> ?, 9\) , in which the gases are completely mixed. 
When the vessels are equal this takes the simple form 

( , / 2SDpA 

52. In the case just treated there is no transmission of energy, so that the 
fundamental hypotheses are fully admissible. In general, however, it is not so. 
The result of § 41, properly modified to apply to the present question, shows 
that the energy which, on the whole, passes positively across the section x is, 
per unit area per second, 



4 V l h + h 2 J 6 A ll ^ 3 2 ^ i} 



This, of course, in general differs from section to section, and thus a disturbance 
of temperature takes place. In such a case we can no longer assume that 
h x and h 2 are absolute constants ; and thus terms in <&$ would come in ; just as 
a term in C 5 appeared in the expression for energy conducted (§ 42). Thus, in 
order that our investigation may be admissible, the process must be conducted 
at constant temperature. This, in general, presupposes conditions external to 
the apparatus. 

53. Though it appears hopeless to attempt a general solution of equation 
(10), we can obtain from it (at least approximately) the conditions for a steady 
state of motion such as must, we presume, finally set in between two infinite 
vessels filled with different gases at the same temperature and pressure. For 
the left-hand member is then an (unknown) constant, a second constant is 
introduced by integrating once with respect to x ; and these, which determine 
the complete solution, are to be found at once by the terminal conditions 



1 dG, f n for x = , ) /1 -, N 



And, by a slight but obvious modification of the latter part of § 51 above, we 
can easily extend the process to the case in which the vessels are of finite 
size : — always, however, on the assumption that their contents may be regarded 
as promptly assuming a state of uniform mixture. The consideration of § 52, 
however, shows that the whole of the contents must be kept at constant temper- 
ature, in order that this result may be strictly applicable. 

54. Recurring to the special case of § 51, let us now suppose that, while 
the masses of the particles remain equal, their diameters are different in the 
two gases. Thus, suppose s x >s 2 . Then it is clear that 

s-f—s'*, and s 2 — s 2 , 



272 PROFESSOR TAIT ON THE 

are both positive. In this case, infinite terminal vessels being supposed, (10) 
gives for the steady state 



A = 



jA h i c i ( n * i ^i \ 1 dn i . n <n 



imjh 

whose integral, between limits as in (11) above, is 

.,_ P j Sn /it Cjnf 1 1 2^' Sj _ 2s 2 2 sA 1 

irnjh I 4s 2 V 2 + 3 V* 2 -^ 2 s i 2 -* 2 (% 2 -s 2 ) 2 s + (s 2 -s 2 2 ) 2 S s)] " 

Here A is the rate of passage of the first gas, in mass per second per unit area 
of the section of the tube. 
If now we put 

then, -when o- is small compared with s, the multiplier of C-^z/3 is 

(l + o- 2 /3s 2 )/s 2 , near i y< 

When a- is nearly equal to s, i.e. one of the sets of particles exceedingly small 
compared with the other, it is nearly 

1-283/s 2 . 

Thus it appears that a difference in size, the mean of the diameters being 
unchanged, favours diffusion. 
Suppose, for instance, 

s 1 : s : s 2 : : 3 : 2 : 1 , 

and we have 

P (3 Ar 2C, / 4 , 36 . 3,4, 1\ ) 

^{3 /» + o ll . 086 ) p_ 1<24 

UV 2+3 1UyD j ~ tt^X ' 



A=- 



7r/s 2 ^/A 

= — /* 1-83. 

Compare this with the result for equal particles (§ 51), remembering that X 
now stands for the mean free path of a particle of either gas in a space filled 
with the other : — and we see that (so long at least as the masses are equal) 
diffusion depends mainly upon the mean of the diameters, being but little 
affected by even a considerable disparity in size between the particles of the 
two gases. Thus it appears that the viscosity and (if the experimental part of 
the inquiry could be properly carried out) conductivity give us much more 
definite information as to the relative sizes of particles of different gases than 
we can obtain from the results of diffusion. 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 273 

Equation (12) shows how the gradient of density of either gas varies, in the 
stationary state, with its percentage in the mixture. For the multiplier of 

-r^ is obviously a maximum when 

dx J 

i i 



s^ + ys-f s 2 +s 2 2 /y' 

in which y=n 1 ln 2 , is so. This condition gives 

n 1 /n 2 =y=s 2 fs 1 . 

Hence the gradient is least steep at the section in which the proportion of the 
two gases is inversely as the ratio of the diameters of their particles ; and it 
increases either way from this section to the ends of the tube, at each of which 
it has the same (greatest) amount. This consideration will be of use to the full 
understanding of the more complex case (below) in which the masses, as well as 
the diameters, of the particles differ in the two gases. 

55. Let us now suppose the mass per particle to be different in the two 
gases. The last terms of the right-hand side of (10), viz., 

may be written in the form 

P, dn^ jn-njhzr* f(y)dy + nfa r°° f(y)dy , 

37m dX \ Jkl ^^M 2 F(2/) + (»-%)VF(y^) ^U(^-* 2 %)+* 2 ^^)| 

where the meanings off and F are as in § 34. 

If we confine ourselves to the steady state, we may integrate (10) directly 
with respect to x, since dQJdt is constant. In thus operating on the part just 
written, the integration with regard to x (with the limiting conditions as in (11)) 
can be carried out under the sign of integration with respect to y : — and then 
the y integration can be effected by quadratures. 

The form of the x integral is the same in each of the terms. For 



I (n-njtini _ I n x dt^ __ n j 1 , A ^ 

Jn Aiii + Bin-nJ J H A(n-n 1 )+Bn 1 A-B ( A-B b 



B 



This expression is necessarily negative, as A and B are always positive. When 
A and B are nearly equal, so that B = (l + e)A, its value is 

A\2 3^ /' 
so that, even when A and B are equal, there is no infinite term. 



274 PROFESSOR TAIT ON THE 

It is easy to see, from the forms of F(z/), and of its first two differential co- 
efficients, that the equation 



h 2 smy)=K^{yJ^) 



can hold for, at most, one finite positive value of y. 

56. As a particular, and very instructive case, let us suppose 

the case of oxygen and hydrogen. 

(a) First, assume the diameters to be equal. Then the integral of (10), 
with limits as in (11), taken on the supposition that the flow is constant, is 

A f, J8 ,^ 1 / T'/ /W-W(1) | FWW-1^(|)/(|) | 16F(|) 

As remarked above, the definite integral is essentially negative. For so is 
every expression of the form 

a — b , Aa — Bb, B 

J I OCT 

A-B^(A-B)2 b A 
provided A, B, a, and b be all positive. When A and B are equal its value is 

I have made a rough attempt at evaluation of the integral, partly by calcu- 
lation, partly by a graphic method. My result is, at best, an approximation, 
for the various instalments of the quadrature appear as the relatively small 
differences of two considerable quantities. Thus the three decimal places, to 
which, from want of leisure, I was obliged to confine myself, are not sufficient 
to give a very exact value. The graphical representations of my numbers were, 
however, so fairly smooth that there seems to be little risk of large error. 
The full curve in the sketch below shows (on a ten-fold scale) the values of 
the integrand (with their signs changed), as ordinates, to the values of y as 
abscissa. The area is about — 2'165. Hence we have 

l ^r = — ?V 3 ' 463 ' 

at irs z Jh t 



(b) Suppose next that the diameter of a Pj is three times that of a P 2 , but 
s 
form 



the semi-sum of the diameters is s as before. The definite integral takes the 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 275 



/ 



. m Mi) jmm <«(*) jogKg. «({)| 



>)-16f(|) F W -4 F (f) (|F W -16F(f)) ! " 9F t"» (F W -4F(|)y * F « 

The corresponding- curve is exhibited by the dashed line in the sketch, and its 
area is about —3 '157. Hence, in this case, 

1 I' = - -TTT 3 " 793 • 



F!bi mm ^h ■»■ ^fi nai 



(c) Still keeping the sum of the semidiameters the same, let the diameter of 
a P 2 be three times that of a P r The integral is 



r 



dy 
o 



Ay) 



U/(i) \^V)m , 6«\f) 576F(|V(f), 36F(f)1 

4- lOfT — - - - I lop 2 L 



+ T-1 r9 l0 g xv\ --, " , l0 S" 



1^)-16F(-|-) F„)-36F(|) (^F(,)-16F(f ))' ^ (F<y)-36F(f )) 



?(y) 



The curve is the dotted line in the cut, and its area is about — 1*7 13. Hence 
we have 

/*!i ] 1 3.312 

dt TTH" ^'/t^ 

If we compare these values, obtained on such widely different assumptions as 
to the relative diameters of the particles, we see at once how exceedingly 
difficult would be the determination of diameters from observed results as to 
diffusion. (Compare § 54.) 

VOL. XXXIIT. PART II. 2 R 



'27 6 PROFESSOR TAIT ON THE 

But we see also how diffusion varies with the relative size of the particles, 
the sum of the diameters being constant. For the smaller, relatively, are the 
particles of smaller mass (those which have the greater mean-square speed) the 
more rapid is the diffusion. 

And further, by comparison with the results of §§ 51, 54, we see how much 
more quickly a gas diffuses into another of different specific gravity than into 
another of the same specific gravity. 

When the less massive particles are indefinitely small in comparison with 
the others, the diameter of these is s ; and for their rate of diffusion we have 

Z— ■=- ?1 1-26 . 
dt 7rs' 2 Jhj_ 

When it is the more massive particles which are evanescent in size, the 
numerical factor seems to be about 3*48. Hence it would appear that, even in 
the case of masses so different, there is a minimum value of the diffusion- 
coefficient, which is reached before the more massive particles are infinitesimal 
compared with the others. 

[At one time I thought of expressing the results of this section in a form 
similar to that adopted in the expression for D in § 51. It is easy to see that 
the quantity corresponding to A. would now be what may be called the mean 
free path of a single particle of one gas in a space filled with another. Its 
value would be easily calculated by the introduction of h x for h in the factor v 
of the integral 



/ 



while keeping e in terms of h. This involves multiplication of each number in 
the fourth column of the Appendix to Part I. by the new factor e-^-^* 1 hj/h*. 
"Rut, on reflection, I do not see that much would be gained by this.] 



FOUNDATIONS OF THE KINETIC THEORY OF GASES. 



277 



APPENDIX. 

The notation is the same as in the Appendix to Part I. 





X 


3?Aj/An !■ 


c 2 X,/X 2 i 


c 3 X 1 /X 2 


x 5 X 1 /X a 


01 


•000049 


■000005 


•000001 


•oooooo 




•2 


•000758 


•000152 


•000030 


■000001 




•3 


003594 


•001078 


000323 


•000029 




•4 


•010364 


•004146 


•001658 


•000265 




•5 


•022505 


•011252 


•005626 


•001407 




•6 


•040512 


•024307 


•014584 


•005250 




•7 


•063623 


•044536 


•031175 


•015276 




•8 


•089928 


•071942 


•057554 


•036834 




•9 


•116712 


105041 


•094537 


•076575 




1-0 


•141040 


141040 


141040 


•141040 




11 


•160292 


•176321 


193953 


•234683 




1-2 


172656 


■207187 


•248624 


■358019 




1-3 


177229 


•230398 


•299517 


•506184 




1-4 


•174174 


•243844 


•341382 


•669108 




1-5 


164430 


•246645 


•369968 


•832427 




1-6 


•149568 


•239309 


•382894 


•980209 




1-7 


131393 


■223368 


•379726 


1-097407 




1-8 


111654 


•200977 


•361758 


1-172098 




1-9 


091960 


•174724 


•331976 


1-198432 




2-0 


•073480 


•146960 


•293920 


1-175680 




21 


•057015 


•119731 


•251435 


1-108829 




2-2 


•043032 


•094670 


•208274 


1-008046 




2-3 


031579 


•072632 


•167054 


•883714 




2-4 


•022584 


■054202 


•130085 


•749288 




2-5 


•015750 


•039375 


•098438 


•615234 




2-6 


•010686 


•027784 


•072238 


•488332 




2-7 


•007074 


019099 


051567 


•375926 




2-8 


•004536 


012701 


•035563 


•278812 




29 


•002871 


008326 


•024145 


•203063 




3-0 


•001710 


005130 


■015390 


•138510 




31 


•001071 


003320 


010294 


•098925 




3-2 


•000629 


002014 


006445 


•065997 




33 


•000361 


001192 


003935 


•042852 




3-4 


•000211 


000689 


002344 


•027098 




3-5 


•000111 


000389 


001361 


•016671 




36 


000066 


000240 


000865 


-010004 




37 


•000037 


000136 


000505 


•005839 




3-8 






000229 


■003307 




3-9 






000118 


•001798 




4-0 






000062 


•000985 


2-095244 2- 


954862 4- 


630593 


14-624154 



Thus the values of 1? C 2 , C 3 , and C 5 are respectively 0-838, 1-182, 1-852, and 5-849. 



( 279 ) 



XIII. — Tables for Facilitating the Computation of Differential Refraction in 
Position Angle and Distance. By the Hon. Lord M'Laren. 

(Read 6th December 1886.) 

The annexed tables are intended to facilitate the computation of the cor- 
rections for refraction which have to be applied to differential measures, such 
as are made with the micrometer or heliometer. 

Differential measures are of two kinds : — (1) Direct measures of differences 
of right ascension and declination ; and (2) measures of position angle and 
distance. In either case the observer only seeks to determine the relative 
positions of the objects under observation ; and the correction for refraction 
consists in the applying to each reading a quantity representing the difference 
of the separate effects of refraction on the apparent places of the two stars, 
whose relative positions are to be determined. This might be effected by 
computing separately the displacement of each star caused by refraction, and 
taking the difference between these quantities for the required correction. 
But, in practice, the correction for refraction is obtained more easily and more 
accurately by differentiation. 

When the measures to be corrected for refraction are direct measures of 
differences of right ascension and differences of declination, the quantities 
log — and log jj may be tabulated for a given latitude, with the arguments, 
declination, and hour angle. The numerical values of these co-efficients for unit 
of arc (or 1") are to be computed for all possible positions above the horizon ; 

7 T> /7 T? 

and then the correction is at once obtained by taking out log j— and log jj 
from the table and adding to each the logarithm of the number of seconds of 
arc in the corresponding measure. It is intended, in a subsequent paper, to 
submit a specimen of such a table prepared for the latitude of Edinburgh. 

The correction for refraction in the case of observations of position angle 
and distance is a more troublesome matter ; because the various readings of 
the position angles and distances for any pair of stars are not all taken at 
the same elevation above the horizon, and therefore each measure must be 
separately corrected for refraction before it can be combined with the others 
into a mean position angle or mean distance. 

VOL. XXXIII. PART II. 2 S 



280 LORD M'LAREN ON DIFFERENTIAL REFRACTION. 

The analytical investigation of these corrections leads to the following- 
expressions : — 

If we call tt and -k the true and apparent position angles ; A' and A, the 
true and apparent distances of the two stars ; £, the mean zenith distance of 
the field of view ; n, the parallactic angle ; and k, the co-efficient of refraction, 

we have 

•a-' = 7r — k tan 2 £ sin {-k — >i) cos (ir— rj). 
A' = A + K A [1 + tan 2 f cos 2 (« - >?)]. 

In these expressions all the variable quantities are given directly by the 
readings, excepting tan 2 £ and 17, the parallactic angle. Now, the last men- 
tioned quantities are functions of the latitude, declination, and hour angle. 
They can therefore be tabulated for a given latitude, with the arguments, 
declination, and hour angle. The present tables give for the parallel 55° 56' 
(which passes through Edinburgh), and also for 57° 30' the quantities log tan 2 £ 
and n for each ten minutes of hour angle, and for each interval of two degrees 
of declination from 40° north to 90°. The tables include the entire circumpolar 
region of the heavens visible from the respective latitudes, and one or other of 
them may be used for observations taken in any part of Scotland, without 
sensible error. Where great accuracy is desired, a table of differences 
applicable to the particular observatory may be obtained by interpolating 
between the two printed tables. 

The computations for the two tables were made in the following manner : — 
Calling cf> the latitude of the place of observation ; II, the polar distance corre- 
sponding to the interval of declination ; and r the hour angle — the quantities 
£ and n are to be obtained by solving the spherical triangle, whose vertices are 
the pole, the zenith, and the star ; whose sides are polar distance, zenith 
distance, and the co-latitude ; and whose angles are hour angle, azimuth and 
parallactic angle. 

To adapt the solution to logarithmic computation, the auxiliary angles 
M and N were computed for each 10 minutes of hour angle by the formulae 

Sin M = cos sin t. 
Tan N = cotan <p cos r. 

The resulting values of N and log cos M were tabulated, and the final compu- 
tations were made by the formulae 

Cos f = cos M cos (IT - N). 
Cos t] = cotan £ tan (II — N). 

The quantities log tan 2 £ and n were directly computed for each alternate 
column of the tables. The intermediate columns were obtained by interpola- 
tion, checked by independent computation of a sufficient number of tabular 
places to ensure substantial accuracy in the last decimal place. 



TABLE 



CONTAINING 



THE LOGARITHM OF TAN 2 ZENITH DISTANCE 



AND THE 



PARALLACTIC ANGLE 



LATITUDE 55° 56', AND DECLINATION 40° to 90°. 



282 



LOGARITHM OF Tan 2 Z FOE, LAT. 55° 56'. 





10 

20 

30 

40 

50 



1 







1 10 
1 20 



30 
40 
50 



40° 



2 

2 10 

2 20 

2 30 

2 40 

2 50 

3 
3 10 
3 20 

3 30 

3 40 

3 50 

4 

4 10 

4 20 

4 30 

4 40 

4 50 




10 
20 

30 
40 
50 



G 



8-9130 
8-9220 
89310 

89575 
8-9840 
90220 

9-0600 
91066 
9-1532 

9-2013 
92494 
93092 

93490 
9-3974 
9-4458 

9-4942 
9-5426 
9-5888 

96350 
9-6796 
9-7242 

9-7684 
9-8126 
9-8557 

9-8988 
9-9411 
9-9834 

00256 
00678 
0-1091 

01504 
0-1921 
02338 

0-2760 
03182 
03604 

0-4026 



42 c 



8-7840 
87942 
8-8064 

8-8405 
8-8746 
8-9201 

8-9656 
9-0194 
9-0731 

9-1275 
9-1818 
9-2361 

92903 
9-3419 
9-3935 

94439 
9-4942 
9-5421 

9-5900 
9-6359 
9-6818 

9-7267 
9-7715 
9-8109 

9-8583 
9-9005 
9-9426 

9-9845 
0-0263 
0-0673 

01083 
0-1492 
0-1900 

02310 
0-2720 
03129 

0-3539 



44° 


46° 


8-6550 


8-4725 


8-6684 


8-4961 


86818 


8-5197 


8-7235 


8-5751 


8-7652 


8-6304 


8-8182 


8-6989 


8-8712 


8-7674 


8-9321 


8-8393 


8-9930 


8-9112 


9-0536 


8-9791 


9-1142 


9-0469 


9-1729 


9-1113 


9-2316 


9-1757 


9-2864 


9-2337 


9-3412 


9-2917 


9-3935 


93464 


9-4458 


9-4011 



48 c 



94954 

9-5450 

9-5922 
9-6394 

9-6849 
9-7304 
9-7741 

9-8178 
9-8598 
9-9018 

9-9433 

9-9848 
00255 

0-0662 
0-1062 
0-1462 

0-1860 
0-2258 
0-2655 

03052 



9-4522 

9-5033 
9-5513 
9-5993 

9-6455 
9-6917 
9-7356 

9-7794 
9-8215 
9-8636 

99049 
99461 
99862 

0-0263 
0-0656 
0-1048 

01439 
01829 
0-2214 

0-2598 



8-2900 
8-3238 
8-3576 

8-4266 
8-4956 
8-5796 

8-6636 
8-7465 
8-8294 

8-9045 
8-9796 
9-0497 

9-1198 
91810 
92422 

9-2993 
9-3564 
9-4090 

9-4616 
9-5104 
9-5592 

9-6061 
9-6530 
9-6970 

9-7410 
9-7832 
9-8254 

9-8664 
9-9074 
99469 

99864 
0-0249 
0-0634 

0-1010 
0-1400 
0-1772 

0-2144 



50° 



52 c 



7-9968 
8-0544 
8-1119 

8-2260 
8-3401 
8-4493 

8-5585 
8-6571 
87556 

8-8385 
8-9214 
8-9959 

9-0704 
9-1348 
9-1992 

9-2581 
9-3170 
9-3714 

9-4248 
9-4744 
9-5240 

9-5709 
9-6178 
9-6618 

9-7057 

9-7478 
9-7898 

9-8306 
9-8713 
9-9103 

9-9492 
9-9871 
0-0249 

0-0621 
0-0993 
0-1357 

0-1720 



7-7036 
7-7849 
7-8662 

8-0254 
8-1846 
8-3190 

8-4534 
8-5676 
8-6818 

8-7725 
8-8632 
8-9421 

9-0210 
9-0886 
9-1562 

92169 

9-2776 
9-3328 

9-3880 
9-4384 
9-4888 

9-5357 
9-5826 
9-6265 

9-6704 
9-7123 
9-7542 

9-7947 
9-8352 
9-8736 

99120 
9-9492 
9-9864 

0-0225 
0-0586 
00941 

0-1296 



54° 



M. 



7-0560 
7-3145 
7-5730 

7-8225 
8-0720 

8-2258 

8-3796 
8-5021 
8-6246 

8-7203 
8-8160 
8-9016 

8-9872 
9-0560 
9-1248 

9-1859 
9-2470 
9-3025 

9-3580 
9-4081 
9-4581 

9-5051 
9-5520 
9-5957 

9-6394 
9-6808 
9-7222 

9-7621 
9-8019 
9-8397 

9-8775 
99139 
99502 

9-9854 
0-0206 
00549 

0-0893 



24 
23 
23 40 



23 
22 
22 



22 



19 

18 
18 





50 



23 30 
23 20 
23 10 




50 
40 



22 30 
22 20 
10 



22 

21 50 

21 40 

21 30 

21 20 

21 10 

21 

20 50 

20 40 

20 30 

20 20 

20 10 

20 

19 50 

19 40 

19 30 

19 20 

19 10 




50 
40 



18 30 

18 20 

18 10 

18 



Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE, FOR LAT. 55° 56'. 



283 







40° 


4 


2° 


44° 


46° 


48° 


50° 


5 


2° 


54° 






H. 


M. 


































H. 


M. 








C 


0' 


C 


0' 


C 


0' 


C 


0' 


C 


0' 


C 


0' 


o r 


0' 


C 


0' 


24 








10 


5 





5 


48 


6 


35 


8 


25 


10 


15 


13 


45 


17 


15 


27 


6 


23 


50 





20 


10 





11 


35 


13 


10 


16 


50 


20 


30 


27 


30 


34 


30 


54 


12 


23 


40 





30 


14 


40 


16 


51 


19 


6 


23 


13 


27 


19 


35 


22 


43 


22 


61 


6 


23 


30 





40 


19 


20 


22 


11 


25 


2 


29 


35 


34 


8 


43 


11 


52 


14 


68 





23 


20 





50 


22 


59 


26 


3 


29 


7 


33 


58 


38 


49 


47 


25 


56 





69 


36 


23 


10 


1 





26 


38 


29 


55 


33 


12 


38 


21 


43 


30 


51 


38 


59 


46 


71 


12 


23 





1 


10 


29 


47 


33 


7 


36 


27 


41 


31 


46 


35 


54 


8 


61 


41 


71 


46 


22 


50 


1 


20 


32 


56 


36 


19 


39 


42 


44 


41 


49 


40 


56 


38 


63 


36 


72 


19 


22 


40 


1 


30 


35 


11 


38 


34 


41 


56 


46 


40 


51 


24 


57 


52 


64 


20 


72 


12 


22 


30 


1 


40 


37 


26 


40 


48 


44 


10 


48 


39 


53 


8 


59 


6 


65 


4 


72 


5 


22 


20 


1 


50 


39 


11 


42 


27 


45 


43 


50 





54 


16 


59 


47 


65 


17 


71 


51 


22 


10 


2 





40 


56 


44 


6 


47 


16 


51 


20 


55 


24 


60 


27 


65 


30 


71 


36 


22 





2 


10 


42 


9 


45 


12 


48 


14 


52 


4 


55 


54 


60 


38 


65 


22 


71 





21 


50 


2 


20 


43 


22 


46 


17 


49 


12 


52 


48 


56 


24 


60 


48 


65 


14 


70 


23 


21 


40 


2 


30 


44 


15 


47 


2 


49 


48 


53 


13 


56 


37 


60 


44 


64 


52 


69 


40 


21 


30 


2 


40 


45 


8 


47 


46 


50 


24 


53 


37 


56 


50 


60 


40 


64 


30 


68 


57 


21 


20 


2 


50 


45 


40 


48 


11 


50 


41 


53 


44 


56 


47 


60 


23 


63 


59 


68 


11 


21 


10 


3 





46 


12 


48 


35 


50 


58 


53 


51 


56 


44 


60 


6 


63 


28 


67 


25 


21 





3 


10 


46 


29 


48 


46 


51 


3 


53 


46 


56 


29 


59 


40 


62 


51 


66 


31 


20 


50 


3 


20 


46 


46 


48 


57 


51 


8 


53 


41 


56 


14 


59 


14 


62 


14 


65 


37 


20 


40 


3 


30 


46 


53 


48 


58 


51 


2 


53 


27 


55 


52 


58 


41 


61 


30 


64 


45 


20 


30 


3 


40 


47 





48 


58 


50 


56 


53 


13 


55 


30 


58 


8 


60 


46 


63 


52 


20 


20 


3 


50 


46 


56 


48 


49 


50 


41 


52 


51 


55 





57 


30 


59 


59 


62 


52 


20 


10 


4 





46 


52 


48 


39 


50 


26 


52 


28 


54 


30 


56 


51 


59 


12 


61 


52 


20 





4 


10 


46 


40 


48 


21 


50 


2 


51 


58 


53 


54 


56 


8 


58 


21 


60 


52 


19 


50 


4 


20 


46 


28 


48 


3 


49 


38 


51 


28 


53 


18 


55 


24 


57 


30 


59 


53 


19 


40 


4 


30 


46 


10 


47 


40 


49 


9 


50 


49 


52 


38 


54 


37 


56 


36 


58 


52 


19 


30 


4 


40 


45 


52 


47 


16 


48 


40 


50 


9 


51 


58 


53 


50 


55 


42 


57 


50 


19 


20 


4 


50 


45 


24 


46 


45 


48 


5 


49 


34 


51 


12 


52 


59 


54 


45 


56 


47 


19 


10 


5 





44 


56 


46 


13 


47 


30 


48 


58 


50 


26 


52 


7 


53 


48 


55 


43 


19 





5 


10 


44 


26 


45 


39 


46 


52 


48 


16 


49 


39 


51 


15 


52 


50 


54 


39 


18 


50 


5 


20 


43 


56 


45 


5 


46 


14 


47 


33 


48 


52 


50 


23 


51 


52 


53 


34 


18 


40 


5 


30 


43 


21 


44 


26 


45 


30 


46 


45 


48 





49 


25 


50 


50 


52 


27 


18 


30 


5 


40 


42 


46 


43 


46 


44 


46 


45 


57 


47 


8 


48 


28 


49 


48 


51 


19 


18 


20 


5 


50 


42 


6 


43 


3 


44 





45 


7 


46 


13 


47 


29 


48 


45 


50 


11 


18 


10 


6 





41 


26 


42 


20 


43 


14 


44 


16 


45 


18 


46 


30 


47 


42 


49 


3 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



284 



LOGARITHM OF TAK 2 Z FOE LAT. 55° 56'. 







40° 


42° 


44° 


46° 


48° 


50° 


52° 


54° 






H. 


M. 


















H. 


M. 


6 





04026 


03539 


0-3052 


0-2598 


0-2144 


0-1720 


0-1296 


0-0893 


18 





6 


10 


0-4454 


03956 


0-3448 


0-2981 


0-2513 


0-2076 


0-1639 


0-1226 


17 


50 


6 


20 


0-4882 


04363 


03844 


03363 


0-2882 


0-2432 


0-1982 


0-1559 


17 


40 


6 


30 


05323 


0-4789 


04244 


0-3747 


0-3250 


0-2737 


02323 


0-1887 


17 


30 


6 


40 


0-5764 


0-5204 


0-4644 


0-4131 


0-3618 


0-3141 


0-2664 


0-2215 


17 


20 


6 


50 


0-6208 


0-5626 


0-5044 


0-4511 


0-3978 


0-3484 


0-2990 


0-2528 


17 


10 


7 





0-6752 


0-6048 


0-5444 


0-4891 


0-4338 


0-3827 


0-3316 


0-2840 


17 





7 


10 


07115 


0-6483 


0-5850 


0-5276 


0-4702 


0-4173 


0-3644 


0-3102 


16 


50 


7 


20 


0-7578 


0-6917 


0-6256 


0-5661 


0-5066 


04519 


0-3972 


0-3364 


16 


40 


7 


30 


0-8048 


0-7356 


0-6663 


0-6043 


0-5423 


0-4857 


0-4290 


0-3716 


16 


30 


7 


40' 


0-8518 


0-7794 


0-7070 


0-6425 


0-5780 


0-5194 


0-4608 


0-4068 


16 


20 


7 


50 


0-9005 


0-8243 


0-7480 


0-6807 


0-6134 


0-5527 


0-4920 


0-4362 


16 


10 


8 





0-9492 


0-8691 


0-7890 


0-7189 


0-6488 


0-5860 


0-5232 


0-4655 


16 





8 


10 


0-9993 


0-9148 


0-8303 


0-7570 


0-6837 


06186 


0-5534 


0-4939 


15 


50 


8 


20 


1-0494 


09605 


0-8716 


0-7951 


0-7186 


0-6511 


0-5836 


0-5222 


15 


40 


8 


30 


1-1009 


1-0069 


0-9128 


0-8329 


0-7529 


0-6828 


0-6127 


0-5494 


15 


30 


8 


40 


1-1524 


1-0532 


0-9540 


0-8706 


0-7972 


0-7145 


0-6418 


0-5766 


15 


20 


8 


50 


1-2045 


1-0995 


0-9944 


0-9078 


08203 


0-7449 


06696 


0-6023 


15 


10 


9 





1-2566 


1-1457 


1-0348 


0-9441 


0-8534 


0-7754 


0-6974 


0-6279 


15 





9 


10 


1-3099 


1-1927 


1-0754 


0-9804 


0-8854 


0-8046 


0-7237 


0-6523 


14 


50 


9 


20 


1-3632 


1-2396 


11160 


1-0167 


0-9174 


0-8337 


0-7500 


0-6766 


14 


40 


9 


30 


1-4166 


1-2857 


1-1548 


1-0513 


0-9477 


0-8611 


0-7744 


0-6989 


14 


30 


9 


40 


1-4700 


1-3318 


1-1936 


1-0858 


0-9780 


0-8884 


0-7988 


0-7211 


14 


20 


9 


50 


1-5228 


1-3765 


1-2303 


1-1181 


1-0059 


0-9136 


0-8212 


0-7417 


14 


10 


10 





1-5756 


1-4213 


1-2670 


1-1504 


1-0338 


0-9387 


0-8436 


0-7622 


14 





10 


10 


1-6260 


1-4636 


1-3011 


1-1800 


1-0589 


0-9611 


0-8633 


0-7799 


13 


50 


10 


20 


1-6764 


1-5058 


1-3352 


1-2096 


1-0840 


0-9835 


0-8830 


0-7977 


13 


40 


10 


30 


1-7232 


1-5441 


1-3650 


1-2355 


1-1059 


1-0030 


0-9000 


0-8131 


13 


30 


10 


40 


1-7700 


1-5824 


1-3948 


1-2613 


1-1278 


1-0224 


0-9170 


0-8285 


13 


20 


10 


50 


1-8101 


1-6149 


1-4197 


1-2826 


1-1454 


1-0379 


0-9305 


0-8406 


13 


10 


11 





1-8502 


1-6474 


1-4446 


1-3038 


11630 


10535 


0-9440 


0-8526 


13 





11 


10 


1-8817 


1-6726 


1-4636 


1-3199 


1-1762 


1-0652 


0-9541 


0-8618 


12 


50 


11 


20 


1-9132 


1-6979 


1-4826 


1-3360 


1-1894 


1-0768 


0-9642 


0-8710 


12 


40 


11 


30 


1-9314 


1-7123 


1-4931 


1-3450 


11969 


1-0832 


0-9695 


0-8761 


12 


30 


11 


40 


1-9496 


1-7266 


1-5036 


1-3540 


1-2044 


1-0896 


0-9748 


0-8812 


12 


20 


11 


50 


1-9581 


1-7333 


1-5084 


1-3580 


1-2076 


1-0925 


0-9773 


0-8831 


12 


10 


12 





1-9666 


1-7399 


1-5132 


1-3620 


1-2108 


10953 


0-9798 


0-8849 


12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE, FOR LAT. 55° 56'. 



285 







40° 


4 


2° 


44° 


46° 


48° 


50° 


52° 


54° 






H. 


M. 


























H. 


M. 


6 





41 c 


26' 


42 c 


20' 


43° 14' 


44 c 


'16' 


45° 18' 


46 c 


30' 


47° 42' 


49° 3' 


18 





6 


10 


40 


41 


41 


33 


42 25 


43 


23 


44 21 


45 


24 


46 26 


47 48 


17 


50 


6 


20 


39 


56 


40 


46 


41 36 


42 


30 


43 24 


44 


17 


45 10 


46 33 


17 


40 


6 


30 


39 


9 


39 


55 


40 40 


41 


32 


42 23 


43 


18 


44 13 


45 28 


17 


30 


6 


40 


38 


22 


39 


3 


39 44 


40 


33 


41 22 


42 


19 


43 16 


44 20 


17 


20 


6 


50 


37 


30 


38 


9 


38 47 


39 


33 


40 18 


41 


12 


42 5 


43 6 


17 


10 


7 





36 


38 


37 


14 


37 50 


38 


32 


39 14 


40 


4 


40 54 


41 52 


17 





7 


10 


35 


44 


36 


18 


36 51 


37 


31 


38 10 


38 


57 


39 43 


40 38 


16 


50 


7 


20 


34 


50 


35 


21 


35 52 


36 


29 


37 6 


37 


49 


38 32 


39 23 


16 


40 


7 


30 


33 


49 


34 


17 


34 45 


35 


20 


35 54 


36 


36 


37 18 


38 5 


16 


30 


7 


40 


32 


48 


33 


13 


33 38 


34 


10 


34 42 


35 


23 


36 4 


36 47 


16 


20 


7 


50 


31 


47 


32 


11 


32 35 


33 


2 


33 29 


34 


9 


34 49 


35 30 


16 


10 


8 





30 


46 


31 


9 


31 32 


31 


54 


32 16 


32 


55 


33 34 


34 13 


16 





8 


10 


29 


42 


30 


9 


30 25 


30 


48 


31 10 


31 


44 


32 16 


32 55 


15 


50 


8 


20 


28 


38 


29 


8 


29 18 


29 


41 


30 4 


30 


33 


31 2 


31 36 


15 


40 


8 


30 


27 


31 


27 


54 


28 6 


28 


28 


28 49 


29 


16 


29 43 


30 15 


15 


30 


8 


40 


26 


23 


26 


39 


26 54 


27 


14 


27 34 


27 


59 


28 24 


28 54 


15 


20 


8 


50 


25 


13 


25 


26 


25 39 


25 


59 


26 18 


26 


42 


27 5 


27 32 


15 


10 


9 





24 


2 


24 


13 


24 24 


24 


43 


25 2 


25 


24 


25 46 


26 10 


15 





9 


10 


22 


28 


23 


15 


23 12 


23 


28 


23 43 


24 


3 


24 23 


24 47 


14 


50 


9 


20 


21 


53 


22 


17 


22 


22 


12 


22 24 


22 


42 


23 


23 23 


14 


40 


9 


30 


20 


29 


20 


46 


20 42 


20 


54 


21 5 


21 


21 


21 37 


21 57 


14 


30 


9 


40 


19 


3 


19 


14 


19 24 


19 


35 


19 46 


20 





20 14 


20 30 


14 


20 


9 


50 


17 


47 


17 


56 


18 4 


18 


15 


18 26 


18 


39 


18 51 


19 7 


14 


10 


10 





16 


30 


16 


37 


16 44 


16 


55 


17 6 


17 


17 


17 28 


17 44 


14 





10 


10 


15 


8 


15 


18 


15 27 


15 


34 


15 41 


15 


51 


16 1 


16 15 


13 


50 


10 


20 


13 


46 


13 


58 


14 10 


14 


13 


14 16 


14 


25 


14 34 


14 45 


13 


40 


10 


30 


12 


26 


12 


28 


12 30 


12 


42 


12 53 


12 


58 


13 11 


13 21 


13 


30 


10 


40 


11 


6 


10 


58 


10 50 


11 


10 


11 30 


11 


30 


11 48 


11 56 


13 


20 


10 


50 


9 


40 


9 


40 


9 40 


9 


52 


10 3 


10 


7 


10 19 


10 26 


13 


10 


11 





8 


14 


8 


22 


8 30 


8 


33 


8 36 


8 


43 


8 50 


8 55 


13 





11 


10 


6 


52 


7 





7 8 


7 


6 


7 3 


7 


15 


7 26 


7 32 


12 


50 


11 


20 


5 


30 


5 


38 


5 46 


5 


38 


5 30 


5 


46 


6 2 


6 9 


12 


40 


11 


30 


4 


10 


4 


14 


4 18 


4 


17 


4 15 


4 


23 


4 31 


4 35 


12 


30 


11 


40 


2 


50 


2 


50 


2 50 


2 


55 


3 


3 





3 


3 


12 


20 


11 


50 


1 


25 


1 


25 


1 25 


1 


28 


1 30 


1 


30 


1 30 


1 30 


12 


10 


12 









































12 






Horizontal Argument, Declination.— Vertical Argument, Hour Angle. 



286 



LOGARITHM OF TAN 2 Z FOR LAT. 55° 56'. 



H. If. 





10 

20 

30 

40 

50 

1 

1 10 

1 20 



30 
40- 

50 


10 
20 



2 30 
2 40 
2 50 



56 c 




10 
20 

30 
40 
50 



4 

4 10 

4 20 

4 30 

4 40 

4 50 




10 
20 

30 
40 
50 





7-3360 

7-6580 
7-9800 
8-1584 

8-3368 
8-4637 
8-5906 

8-6906 
8-7906 
8-8720 

8-9534 
9-0234 
9-0934 

9-1549 
9-2164 
9-2722 

9-3280 
9-3777 

9-4274 

9-4744 
9-5214 
95649 

9-6084 
9-6493 
9-6902 

9-7294 
9-7686 
9-8058 

9-8430 
9-8785 
99140 

9-9483 
9-9826 
0-0158 

00490 



58° 



7-3788 
7-5880 

7-8240 
8-0600 
8-2095 

8-3590 
8-4772 
8-5953 

8-6891 
8-7828 
8-8625 

8-9422 
9-0103 
9-0783 

9-1382 
9-1981 
9-2545 

93109 
9-3581 
9-4052 

9-4513 
9-4973 
9-5399 

9-5824 
9-6223 
9-6623 

9-7008 
9-7392 
9-7755 

9-8117 
9-8462 
9-8807 

9-9141 
9-9474 
9-9797 

00119 



60° 



7-7420 
7-7905 
7-8390 

7-9895 
8-1398 
8-2605 

8-3812 
8-4906 
8-6000 

8-6875 
8-7750 
8-8530 

8-9310 
8-9971 
9-0632 

9-1251 
9-1798 
9-2368 

9-2938 
9-3384 
9-3830 

9-4281 
9-4732 
9-5148 

9-5564 
9-5954 
9-6344 

9-6721 
9-7098 
9-7451 

9-7804 
98139 
9-8474 

9-8798 
9-9122 
9-9435 

9-9748 



62 c 



64° 



66° 



68 c 



8-0315 
8-0598 
8-0880 

8-1904 

8-2927 
8-3836 

8-4745 
8-5640 
8-6535 

8-7299 
8-8064 
8-8761 

8-9458 
9-0065 
9-0672 

9-1224 
9-1775 
9-2296 

9-2817 
9-3260 
93703 

9-4135 
9-4568 
9-4969 

9-5369 
9-5746 
96123 

96485 
9-6847 
9-7189 

9-7531 

9-7854 
9-8176 

9-8489 
9-8801 
99101 

9-9400 



8-3210 
8-3289 
8-3368 

8-3912 
8-4456 
8-5065 

8-5678 
8-6374 
8-7070 

8-7724 
8-8378 
8-8992 

8-9606 
9-0169 
9-0732 

9-1242 
9-1752 

9-2224 

9-2696 
93136 
9-3576 

9-3990 
9-4404 
9-4789 

9-5174 
9-5538 
9-5902 

9-6249 
9-6596 
9-6927 

9-7258 
9-7568 
9-7878 

9-8170 
9-8480 
9-8766 

9-9052 



8-4923 
8-4978 
8-5033 

8-5439 
8-5844 
8-6307 

8-6769 
8-7310 
8-7850 

8-8394 
8-8937 
8-9465 

8-9993 
9-0483 
9-0973 

9-1429 
9-1885 
9-2317 

9-2748 
9-3154 
9-3560 

9-3972 
9-4384 
9-4721 

9-5057 
9-5401 
9-5744 

9-6025 
9-6405 
9-6716 

9-7027 
9-7325 
9-7622 

9-7907 
9-8192 
9-8464 

9-8736 



8-6636 
8-6667 
8-6698 

8-6965 
8-7232 
8-7546 

8-7860 
8-8245 
8-8630 

8-9063 
8-9496 
8-9938 

9-0380 
9-0797 
9-1214 

9-1616 
9-2018 
9-2409 

9-2800 
9-3172 
9-3544 

9-3904 
9-4264 
9-4602 

9-4940 
9-5263 
9-5586 

9-5900 
9-6214 
9-6505 

9-6796 
9-7081 
97366 

9-7635 
9-7904 
9-8162 

9-8420 



70° 



8-7936 
8-7952 
8-7967 

8-8164 
8-8360 
8-8606 

8-8851 
8-9161 
89471 

8-9811 
9-0150 
9-0517 

9-0883 
91235 
9-1587 

9-1938 
9-2288 
9-2634 

9-2980 
93313 
9-3645 

93971 

9-4297 
9-4604 

9-4911 
9-5209 
9-5506 

9-5796 
96086 
9-6357 

9-6628 
9-6891 
9-7154 

9-7407 
9-7660 
97901 

9-8141 



H. 



M. 



24 

23 50 

23 40 

23 30 

23 20 

23 10 

23 

22 50 

22 40 

22 30 

22 20 

22 10 



22 
21 
21 

21 
21 
21 



19 

18 
18 




50 
40 

30 
20 
10 



21 

20 50 

20 40 

20 30 

20 20 

20 10 

20 

19 50 

19 40 

19 30 

19 20 

19 10 




50 
40 



18 30 

18 20 

18 10 

18 



Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOR LAT. 55° 56'. 



287 





56° 


58° 


60° 


62° 


64° 


66° 


68° 


70° 






H. M. 


















H. 


M. 





180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


24 





10 


90 


137 2 


158 40 


167 30 


168 22 


172 50 


174 32 


174 58 


23 


50 


20 


88 56 


118 24 


147 42 


155 


162 16 


165 40 


169 4 


169 55 


23 


40 


30 


87 46 


111 38 


135 29 


144 42 


152 59 


157 14 


161 29 


163 29 


23 


30 


40 


86 36 


104 51 


123 6 


134 24 


143 42 


148 48 


153 54 


157 3 


23 


20 


50 


85 25 


101 11 


116 56 


127 35 


137 13 


142 49 


148 25 


151 56 


23 


10 


1 


84 14 


97 30 


110 46 


120 45 


130 44 


136 50 


142 56 


146 49 


23 





1 10 


83 8 


94 50 


106 32 


115 56 


125 21 


131 39 


137 57 


142 5 


22 


50 


1 20 


82 2 


92 10 


102 18 


111 7 


119 58 


126 28 


132 58 


137 20 


22 


40 


1 30 


80 56 


90 5 


99 10 


107 29 


115 45 


122 10 


128 34 


133 10 


22 


30 


1 40 


79 50 


88 


96 10 


103 51 


111 32 


117 51 


124 10 


128 59 


22 


20 


1 50 


78 46 


86 14 


93 41 


100 52 


108 3 


114 10 


120 17 


125 9 


22 


10 


2 


77 42 


84 27 


91 12 


97 53 


104 34 


110 29 


116 24 


121 19 


22 





2 10 


76 38 


82 52 


89 6 


95 23 


101 39 


107 21 


113 3 


117 55 


21 


50 


2 20 


75 34 


81 17 


87 


92 52 


98 44 


104 13 


109 42 


114 31 


21 


40 


2 30 


74 29 


79 49 


85 8 


90 39 


96 10 


101 26 


106 41 


111 24 


21 


30 


2 40 


73 24 


78 20 


83 16 


88 26 


93 36 


98 38 


103 40 


108 17 


21 


20 


2 50 


72 23 


76 59 


81 35 


86 26 


91 14 


96 6 


100 55 


105 25 


21 


10 


3 


71 12 


75 38 


79 54 


84 26 


88 58 


93 34 


98 10 


102 33 


21 





3 10 


70 11 


74 26 


78 15 


82 34 


87 52 


91 16 


95 40 


99 56 


20 


50 


3 20 


69 


72 48 


76 36 


80 41 


84 46 


88 58 


93 10 


97 18 


20 


40 


3 30 


67 54 


71 30 


75 3 


78 55 


82 47 


86 48 


90 49 


94 49 


20 


30 


3 40 


66 48 


70 11 


73 30 


77 9 


80 48 


84 37 


88 28 


92 19 


20 


20 


3 50 


65 40 


68 51 


72 


75 28 


78 56 


82 36 


86 16 


89 59 


20 


10 


4 


64 32 


67 31 


70 30 


73 47 


77 4 


80 34 


84 4 


87 39 


20 





4 10 


63 24 


66 14 


69 4 


72 11 


75 17 


78 38 


81 58 


85 26 


19 


50 


4 20 


62 16 


64 57 


67 38 


70 34 


73 30 


76 41 


79 52 


83 12 


19 


40 


4 30 


61 7 


63 39 


66 11 


68 59 


71 46 


74 49 


77 50 


81 4 


19 


30 


4 40 


59 58 


62 21 


64 44 


67 23 


70 2 


72 56 


75 50 


78 55 


19 


20 


4 50 


58 48 


61 3 


63 19 


65 51 


68 23 


71 9 


73 54 


76 48 


19 


10 


5 


57 38 


59 46 


61 54 


64 19 


66 44 


69 21 


71 58 


74 41 


19 





5 10 


56 27 


58 29 


60 30 


62 48 


65 5 


67 36 


70 7 


72 47 


18 


50 


5 20 


55 16 


57 11 


59 6 


61 16 


63 26 


65 51 


68 16 


70 53 


18 


40 


5 30 


54 3 


55 53 


57 42 


59 46 


61 50 


64 8 


66 26 


68 52 


18 


30 


5 40 


52 50 


54 34 


56 18 


58 16 


60 14 


62 25 


64 36 


66 51 


18 


20 


5 50 


51 37 


53 16 


54 55 


56 47 


58 39 


60 14 


62 48 


65 2 


18 


10 


6 


50 24 


51 58 


53 32 


55 18 


57 4 


59 2 


61 


63 13 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 
VOL. XXXIII. PART II. 



2 T 



•_>ss 



LOGARITHM OF Tan 2 Z FOR LAT. 55° 56'. 







56° 


58° 


60° 


62° 


64° 


66° 


68° 


70° 






H. 


M. 


















H. 


M. 


6 





0-0490 


0-0119 


9-9748 


9-9400 


9-9052 


9-8736 


9-8420 


9-8141 


18 





6 


10 


0-0813 


0-0428 


0-0043 


9-9684 


9-9325 


9-8995 


9-8665 


9-8369 


17 


50 


6 


20 


0-1136 


0-0737 


0-0338 


9-9968 


9-9598 


9-9254 


9-8910 


9-8598 


17 


40 


6 


30 


0-1451 


0-1039 


00627 


0-0245 


9-9862 


9-9505 


9-9147 


9-8821 


17 


30 


6 


40 


0-1766 


0-1341 


0-0916 


0-0521 


0-0126 


9-9755 


9-9384 


9-9043 


17 


20 


6 


50 


0-2065 


0-1629 


0-1194 


0-0786 


0-0377 


9-9993 


99609 


9-9254 


17 


10 


7 





02364 


0-1918 


0-1572 


0-1050 


00628 


0-0231 


9-9834 


9-9464 


17 





7 


10 


0-2660 


0-2199 


0-1738 


0-1304 


0-0869 


0-0459 


0-0048 


9-9663 


16 


50 


7 


20 


0-2956 


0-2480 


0-2004 


0-1557 


o-iiio 


0-0686 


0-0262 


9-9862 


16 


40 


7 


30 


0-3242 


0-2752 


0-2261 


0-1799 


0-1337 


0-0902 


0-0466 


0-0052 


16 


30 


7 


40' 


0-3528 


0-3023 


0-2518 


0-2041 


0-1562 


0-1117 


0-0670 


0-0242 


16 


20 


7 


50 


03803 


0-3284 


0-2764 


0-2274 


0-1784 


0-1323 


0-0861 


0-0422 


16 


10 


8 





0-4078 


0-3544 


0-3010 


0-2507 


0-2004 


0-1528 


0-1052 


0-0599 


16 





8 


10 


0-4343 


0-3793 


0-3243 


0-2727 


0-2210 


0-1721 


0-1232 


0-0765 


15 


50 


8 


20 


0-4608 


0-4042 


0-3476 


0-2946 


0-2416 


0-1914 


0-1412 


0-0931 


15 


40 


8 


30 


0-4861 


0-4279 


0-3696 


0-3153 


0-2609 


0-2094 


0-1578 


0-1086 


15 


30 


8 


40 


0-5114 


0-4515 


0-3916 


0-3359 


0-2802 


0-2273 


0-1744 


0-1240 


15 


20 


8 


50 


0-5349 


0-4736 


0-4122 


0-3551 


02980 


0-2439 


0-1897 


0-1382 


15 


10 


9 





0-5584 


0-4956 


0-4328 


0-3743 


0-3158 


0-2604 


0-2050 


0-1524 


15 





9 


10 


0-5808 


0-5163 


0-4518 


0-3920 


0-3322 


0-2754 


0-2191 


0-1655 


14 


50 


9 


20 


06032 


0-5370 


0-4708 


0-4097 


0-3486 


02909 


0-2332 


0-1785 


14 


40 


9 


30 


0-6233 


0-5557 


0-4881 


0-4257 


3632 


0-3046 


0-2460 


0-1903 


14 


30 


9 


40 


0-6434 


0-5744 


0-5054 


0-4416 


0-3778 


0-3183 


0-2588 


0-2020 


14 


20 


9 


50 


0-6621 


0-5910 


0-5208 


0-4559 


0-3900 


0-3304 


0-2699 


0-2121 


14 


10 


10 





0-6808 


0-6085 


0-5362 


0-4701 


0-4040 


0-3425 


0-2810 


0'2222 


14 





10 


10 


0-6966 


0-6229 


05493 


0-4823 


0-4152 


0-3528 


0-2903 


0-2309 


13 


50 


10 


20 


0-7124 


06374 


0-5624 


0-4944 


0-4264 


0-3630 


0-2999 


0-2395 


13 


40 


10 


30 


0-7262 


0-6499 


0-5737 


0-5048 


0-4359 


0-3719 


0-3078 


0-2469 


13 


30 


10 


40 


0-7400 


06625 


0-5850 


0-5152 


0-4454 


0-3807 


03160 


0-2543 


13 


20 


10 


50 


0-7506 


06722 


0-5938 


0-5232 


0-4526 


0-3873 


0-3221 


0-2600 


13 


10 


11 





0-7612 


0-6819 


0-6026 


0-5312 


0-4598 


0-3940 


0-3282 


0-2657 


13 





11 


10 


0-7695 


0-6894 


0-6093 


0-5374 


0-4655 


03992 


0-3327 


0-2699 


12 


50 


11 


20 


0-7778 


0-6969 


0-6160 


05436 


0-4712 


0-4044 


0-3372 


02740 


12 


40 


11 


30 


0-7827 


0-7011 


0-6195 


0-5466 


0-4737 


0-4068 


03397 


0-2760 


12 


30 


11 


40 


0-7876 


0-7053 


0-6230 


05496 


0-4762 


0-4092 


0-3422 


0-2783 


12 


20 


11 


50 


0-7888 


0-7067 


0-6246 


0-5512 


0-4778 


0-4105 


03432 


02793 


12 


10 


12 





0-7900 


0-7081 


0-6262 


0-5528 


04794 


0-4118 


0-3442 


02803 


12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PAEALLACTIC ANGLE FOE LAT. 55° 56'. 



289 







56° 


58° 


60° 


6 


2° 


64° 


66° 


68° 


71 


3° 






H. 


M. 


































H. 


M. 


6 





50° 


24' 


51° 


58' 


53° 


32' 


55° 


18' 


57° 


4' 


59° 


2' 


61° 


0' 


63° 


13' 


18 





6 


10 


49 


10 


50 


39 


52 


7 


53 


48 


55 


29 


57 


22 


59 


15 


61 


22 


17 


50 


6 


20 


47 


56 


49 


19 


50 


42 


52 


18 


53 


54 


55 


42 


57 


30 


59 


31 


17 


40 


6 


30 


46 


40 


47 


59 


49 


17 


50 


49 


52 


20 


54 


3 


55 


45 


57 


42 


17 


30 


6 


40 


45 


24 


46 


38 


47 


52 


49 


19 


50 


46 


52 


23 


54 





55 


52 


17 


20 


6 


50 


44 


7 


45 


17 


46 


26 


47 


49 


49 


12 


50 


45 


52 


18 


54 


3 


17 


10 


7 





42 


50 


43 


55 


45 





46 


19 


47 


38 


49 


7 


50 


36 


52 


14 


17 





7 


10 


41 


32 


42 


34 


43 


36 


44 


50 


46 


4 


47 


29 


48 


53 


50 


28 


16 


50 


7 


20 


40 


14 


41 


13 


42 


12 


43 


21 


44 


30 


45 


50 


47 


10 


48 


42 


16 


40 


7 


30 


38 


52 


39 


49 


40 


46 


41 


50 


42 


53 


44 


11 


45 


29 


46 


56 


16 


30 


7 


40 


37 


30 


38 


25 


39 


20 


40 


18 


41 


16 


42 


32 


43 


48 


45 


10 


16 


20 


7 


50 


36 


11 


37 


12 


37 


53 


38 


50 


39 


46 


40 


56 


42 


6 


43 


25 


16 


10 


8 





34 


52 


35 


59 


36 


26 


37 


21 


38 


16 


39 


20 


40 


24 


41 


39 


16 





8 


10 


33 


31 


34 


25 


34 


59 


35 


51 


36 


42 


37 


43 


38 


43 


39 


54 


15 


50 


8 


20 


32 


10 


32 


51 


33 


32 


34 


20 


35 


8 


36 


5 


37 


2 


38 


8 


15 


40 


8 


30 


30 


47 


31 


25 


32 


3 


32 


49 


33 


34 


34 


27 


35 


20 


36 


23 


15 


30 


8 


40 


29 


24 


29 


59 


30 


34 


31 


17 


32 





32 


49 


33 


38 


34 


38 


15 


20 


8 


50 


27 


59 


28 


33 


29 


7 


29 


47 


30 


27 


31 


13 


31 


58 


32 


54 


15 


10 


9 





26 


34 


27 


7 


27 


40 


28 


17 


28 


54 


29 


36 


30 


18 


31 


10 


15 





9 


10 


25 


10 


25 


40 


26 


10 


26 


45 


27 


19 


27 


58 


28 


37 


29 


27 


14 


50 


9 


20 


23 


46 


24 


13 


24 


40 


25 


12 


25 


44 


26 


20 


26 


56 


27 


43 


14 


40 


9 


30 


22 


16 


22 


43 


23 


10 


23 


39 


24 


7 


24 


42 


25 


17 


26 


1 


14 


30 


9 


40 


20 


46 


21 


13 


21 


40 


22 


5 


22 


30 


23 


4 


23 


38 


24 


18 


14 


20 


9 


50 


19 


23 


19 


46 


20 


9 


20 


33 


20 


56 


21 


27 


21 


57 


22 


33 


14 


10 


10 





18 





18 


19 


18 


38 


19 





19 


22 


19 


49 


20 


16 


20 


48 


14 





10 


10 


16 


28 


16 


46 


17 


3 


17 


24 


17 


44 


17 


39 


18 


33 


19 


3 


13 


50 


10 


20 


14 


56 


15 


12 


15 


28 


15 


47 


16 


6 


16 


28 


16 


50 


17 


18 


13 


40 


10 


30 


13 


30 


13 


43 


13 


55 


14 


13 


14 


30 


14 


52 


15 


14 


15 


36 


13 


30 


10 


40 


12 


4 


12 


13 


12 


22 


12 


38 


12 


54 


13 


16 


13 


38 


13 


54 


13 


20 


10 


50 


10 


32 


10 


41 


10 


49 


11 


2 


11 


14 


11 


32 


11 


50 


12 


8 


13 


10 


11 





9 





9 


8 


9 


16 


9 


25 


9 


34 


9 


48 


10 


2 


10 


21 


13 





11 


10 


7 


38 


7 


40 


7 


42 


7 


52 


8 


2 


7 


54 


7 


46 


8 


21 


12 


50 


11 


20 


6 


16 


6 


12 


6 


8 


6 


19 


6 


30 


6 





5 


30 


6 


20 


12 


40 


11 


30 


4 


38 


4 


40 


4 


42 


4 


48 


4 


53 


4 


38 


4 


23 


4 


52 


12 


30 


11 


40 


3 





3 


8 


3 


16 


3 


16 


3 


16 


3 


16 


3 


16 


3 


23 


12 


20 


11 


50 


1 


30 


1 


34 


1 


38 


1 


38 


1 


38 


1 


38 


1 


38 


1 


42 


12 


10 


12 





















































12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



290 



LOGARITHM OF Tan 2 Z FOR LAT. 55° 56'. 




10 
20 



30 
40 
50 



1 

1 10 

1 20 

1 30- 

1 40 

1 50 

2 
2 10 
2 20 



30 
40 
50 


10 
20 



3 30 

3 40 

3 50 

4 
4 10 
4 20 

4 30 

4 40 

4 50 




10 
20 

30 
40 
50 





72° 


74° 


8-9212 


9-0240 


8-9226 


9-0251 


8-9240 


90262 


8-9362 


9-0356 


8-9488 


90452 


8-9665 


9-0585 


8-9842 


9-0717 


9-0077 


9-0901 


9-0312 


9-1084 


9-0558 


9-1284 


9-0804 


9-1484 


91095 


9-1717 


9-1386 


9-1950 


91673 


9-2193 


9-1960 


9-2435 


9-2259 


9-2686 


9-2558 


9-2936 


9-2859 


9-3189 


93160 


93443 


93453 


9-3695 


9-3746 


9-3948 


9-4038 


9-4201 


9-4330 


9-4454 


9-4606 


9-4699 


9-4882 


9-4945 


9-5154 


9-5184 


9-5426 


9-5423 


9-5692 


9-5662 


9-5958 


9-5900 


9-6209 


9-6128 


96460 


9-6351 


9-6701 


96569 


96942 


9-6788 


9-7179 


97002 


97416 


9-7215 


97639 


9-7419 


97862 


97623 



76° 



78° 



9-1268 
9-1276 
9-1284 

9-1350 
9-1416 
9-1504 

9-1592 
9-1724 
9-1856 

9-2010 
9-2164 
9-2339 

9-2514 
9-2712 
92910 

9-3112 
9-3314 
9-3520 

9-3726 
9-3938 
9-4150 

9-4364 
9-4578 
9-4793 

9-5008 
9-5214 
9-5420 

95631 

9-5842 
9-6042 

96242 
5-6438 
96634 

9-6824 
9-7014 
9-7199 

97384 



92140 
9-2144 
9-2148 

9-2198 
9-2248 
9-2319 

9-2390 
9-2493 
9-2595 

9-2712 
9-2828 
9-2966 

93103 
9-3262 
9-3421 

9-3584 
9-3747 
93915 

9-4083 
9-4259 
9-4435 

9-4615 

9-4795 
9-4973 

9-5150 
9-5327 
9-5503 

9-5681 
9-5859 
9-6032 

9-6205 
96375 
96544 

96709 
9-6874 
97036 

97197 



80° 


82° 


84° 


86° 


9-3012 


9-3781 


9-4550 


9-5240 


9-3012 


9-3781 


9-4550 


9-5240 


9-3012 


9-3781 


9-4550 


9-5240 


9-3046 


9-3807 


9-4568 


9-5257 


9-3080 


9-3833 


9-4586 


9-5268 


93134 


9-3869 


9-4604 


9-5279 


9-3188 


9-3905 


9-4622 


9-5291 


9-3261 


9-3957 


9-4653 


9-5310 


93334 


9-4009 


9-4684 


9-5328 


93413 


9-4071 


94729 


9-5358 


9-3492 


9-4133 


9-4774 


9-5387 


93592 


9-4211 


9-4829 


9-5422 


93692 


9-4288 


9-4884 


9-5457 


9-3812 


9-4327 


9-4942 


9-5495 


93932 


9-4366 


9-5000 


9-5532 


9-4056 


9-4508 


9-5059 


9-5572 


9-4180 


94649 


9-5118 


9-5612 


9-4310 


9-4751 


9-5191 


9-5658 


9-4440 


9-4852 


9-5264 


9-5704 


9-4580 


9-4958 


95336 


9-5752 


9-4720 


9-5064 


9-5408 


9-5799 


9-4866 


95178 


9-5489 


9-5852 


9-5012 


95291 


9-5570 


9-5905 


95152 


9-5401 


9-5649 


9-5957 


9-5292 


9-5510 


9-5728 


9-6009 


9-5439 


9-5625 


9-5811 


9-6063 


9-5586 


9-5740 


9-5894 


9-6117 


9-5731 


9-5855 


9-5979 


9-6177 


9-5876 


9-5970 


96064 


9-6236 


9-6022 


9-6086 


96149 


9-6316 


9-6168 


9-6201 


96234 


96396 


9-6311 


96317 


9-6322 


9-6427 


96454 


96432 


96410 


9-6457 


9-6594 


96539 


96493 


9-6512 


9-6734 


9-6646 


9-6576 


9-6567 


9-6872 


96764 


9-6665 


9-6627 


9-7010 


9-6882 


96754 


9-6686 



24 

23 50 

23 40 

23 30 

23 20 

23 10 

23 

22 50 

22 40 

22 30 

22 20 

22 10 



22 
21 
21 




50 

40 



21 30 
21 20 
21 10 



21 

20 50 

20 40 

20 30 

20 20 

20 10 

20 

19 50 

19 40 

19 30 

19 20 

19 10 



19 

18 50 
18 40 



30 

20 



18 10 



18 



Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOR LAT. 55° 56' 



291 



M. 





10 

20 

30 

40 

50 

1 
1 10 
1 20 

1 30 

1 40 

1 50 

2 

2 10 

2 20 

2 30 

2 40 

2 50 

3 
3 10 
3 20 



30 
40 
50 


10 

20 



4 30 
4 40 
4 50 




10 
20 

30 
40 
50 





72 c 



180° 0' 
175 50 
170 40 

165 29 
160 12 
155 27 

150 42 
146 12 
141 42 

137 45 
133 48 
130 1 

126 14 
122 47 
119 20 

116 7 
112 54 
109 55 

106 56 

104 11 
101 26 

98 48 
96 10 
93 42 

91 14 
88 53 
86 32 

84 16 
82 
79 50 

77 40 
75 35 
73 30 

71 28 
69 26 

67 26 

65 26 



74° 



180° 0' 
175 55 
171 20 

166 42 
162 
157 42 

153 24 
149 43 
146 2 

141 43 
137 24 
133 46 

130 7 
126 43 
123 18 

120 7 
116 55 
113 53 

110 55 
108 7 
105 18 

102 36 
99 54 
97 22 

94 49 
92 22 

89 54 

87 34 
85 13 
82 57 

80 41 
78 10 
75 29 

73 46 

72 2 
70 27 

68 52 



76° 



180° 0' 
176 
172 

167 54 
163 48 

159 57 

156 6 
152 14 

148 22 

144 43 
141 
137 30 

134 

130 38 
127 16 

124 6 
120 56 
117 55 

114 54 
112 2 
109 10 

106 24 
103 38 
101 1 

98 24 
95 51 
93 18 

90 52 
88 26 
86 4 

83 42 
81 25 
79 8 

76 53 
74 38 
72 28 

70 18 



78° 



180° 0' 
176 20 
172 39 

168 54 
165 9 

161 29 

157 48 
154 15 
150 41 

147 12 
143 43 
140 23 

137 3 
133 48 
130 32 

127 25 
124 17 
121 20 

118 23 
115 32 
112 40 

109 54 
107 7 
104 28 

101 49 
99 15 
96 41 

94 10 
91 39 
89 13 

86 47 
84 26 
82 5 

79 46 

77 27 
75 12 

72 57 



80° 



180° 0' 
176 39 
173 18 

169 54 
166 30 
163 

159 30 
156 15 
153 

149 43 
146 26 
143 16 

140 6 
136 57 
133 48 

130 43 
127 38 
124 45 

121 52 



180° 0' 
176 48 
173 35 

170 24 
167 12 
164 3 

160 53 
158 19 
154 44 

151 37 
148 29 
145 56 

142 23 
139 23 
136 23 



119 


1 


116 


10 


113 


23 


110 


36 


107 


55 


105 


14 


102 


39 


100 


3 


97 


28 


94 


51 


92 


22 


89 


52 


87 


27 


85 


2 


82 


39 


80 


16 


77 


56 



84° 



180° 0' 
176 56 
173 52 



170 53 171 34 



86° 



180° 0' 
177 13 
174 26 



75 36 



LJ6 


VI 


130 


31 


127 


41 


124 


50 


122 


3 


119 


15 


116 


30 


113 


45 


111 


5 


108 


25 


105 


49 


103 


13 


100 


37 


98 


1 


95 


30 


92 


58 


90 


31 


88 


3 


85 


37 


83 


11 


80 


48 


78 


25 



167 54 
165 5 

162 16 
159 22 
156 28 

153 30 
150 32 
147 36 

144 40 
141 49 
138 58 

136 11 
133 24 
130 36 

127 48 
125 4 
122 20 



168 42 
165 59 

163 16 
160 32 

157 47 

154 58 
152 8 
149 21 

146 33 
143 50 

141 6 

138 24 
135 42 
133 

130 18 
127 39 
125 



119 


37 


122 


21 


116 


54 


119 


41 


114 


15 


116 


58 


111 


36 


114 


14 


108 


59 


111 


47 


106 


22 


109 


19 


103 


46 


106 


45 


101 


10 


104 


10 


98 


37 


101 


38 


96 


4 


99 


5 


93 


34 


96 


35 


91 


4 


94 


4 


88 


35 


91 


34 


86 


6 


89 


4 


83 


40 


86 


36 


81 


14 


84 


8 



M. 



24 
23 50 
23 40 



23 30 
23 20 
23 10 



23 
22 50 
22 40 



22 30 
22 20 
22 10 



22 
21 50 
21 40 



21 
21 
21 



30 
20 
10 



21 

20 50 

20 40 

20 30 

20 20 

20 10 



20 





19 


50 


19 


40 


19 


30 


19 


20 


19 


10 


19 





18 


50 


18 


40 


18 


30 


18 


20 


18 


10 


18 






Horizontal Argument, Declination. 



-Vertical Argument, Hour Angle. 



292 



LOGARITHM OF Tan 2 Z FOR LAT. 55° 56'. 





72° 


74° 


76° 


78° 


80° 


82° 


84° 


86° 






H. M. 


















H. 


M. 


6 


9-7862 


97623 


9-7384 


9-7197 


9-7010 


9-6882 


9-6754 


9-6686 


18 





6 10 


9-8074 


9-7818 


9-7562 


97352 


9-7142 


9-6988 


9-6833 


9-6739 


17 


50 


6 20 


9-8286 


9-8013 


9-7740 


9-7507 


9-7274 


97093 


9-6912 


9-6792 


17 


40 


6 30 


9-8494 


98199 


9-7905 


9-7654 


97403 


97200 


9-6997 


9-6849 


17 


30 


6 40 


9-8702 


9-8386 


9-8070 


9-7801 


9-7532 


9-7307 


9-7082 


9-6905 


17 


20 


6 50 


9-8898 


9-8567 


9-8235 


9-7944 


9-7652 


9-7404 


97155 


96956 


17 


10 


7 


99094 


9-8747 


9-8400 


9-8086 


9-7772 


9-7500 


9-7228 


9-7007 


17 





7 10 


9-9278 


9-8917 


9-8556 


9-8226 


9-7895 


9-7600 


9-7305 


9-7059 


16 


50 


7 20 


9-9462 


9-9087 


9-8712 


9-8365 


9-8018 


9-7700 


9-7382 


97111 


16 


40 


7 30 


9-9638 


9-9247 


9-8855 


9-8492 


9-8128 


9-7790 


9-7452 


9-7157 


16 


30 


7 40 


9-9814 


9-9406 


9-8998 


9-8618 


9-8238 


9-7880 


9-7522 


9-7203 


16 


20 


7 50 


9-9980 


9-9559 


9-9137 


9-8739 


9-8342 


9-7967 


9-7592 


9-7251 


16 


10 


8 


00146 


9-9711 


9-9276 


9-8861 


9-8446 


9-8054 


9-7662 


9-7299 


16 





8 10 


0-0298 


9-9849 


9-9403 


9-8973 


9-8543 


9-8136 


9-7728 


9-7345 


15 


50 


8 20 


0-0450 


9-9987 


9-9530 


9-9085 


9-8640 


9-8217 


9-7794 


9-7390 


15 


40 


8 30 


0-0593 


0-0119 


9-9647 


9-9189 


9-8732 


9-8292 


9-7851 


8-7429 


15 


30 


8 40 


00736 


0-0250 


9-9764 


9-9294 


9-8824 


9-8366 


9-7908 


9-7468 


15 


20 


8 50 


0-0867 


0-0369 


9-9872 


9-9389 


9-8906 


9-8433 


9-7960 


9-7505 


15 


10 


9 


0-0998 


0-0489 


9-9980 


9-9484 


9-8988 


9-8500 


9-8012 


9-7541 


15 





9 10 


0-1118 


0-0598 


0-0078 


9-9571 


9-9064 


9-8564 


9-8064 


9-7576 


14 


50 


9 20 


0-1238 


0-0707 


0-0176 


9-9658 


9-9140 


9-8628 


9-8116 


9-7611 


14 


40 


9 30 


0-1345 


0-0805 


0-0264 


9-9735 


9-9206 


9-8682 


9-8157 


9-7640 


14 


30 


9 40 


0-1452 


0-0902 


0-0352 


9-9812 


9-9272 


9-8735 


9-8198 


9-7669 


14 


20 


9 50 


01543 


0-0986 


00429 


9-9879 


9-9330 


9-8785 


9-8230 


9-7696 


14 


10 


10 


0-1634 


0-1070 


0-0506 


9-9947 


9-9388 


9-8834 


9-8280 


9-7722 


14 





10 10 


0-1714 


0-1141 


0-0567 


0-0002 


9-9436 


9-8874 


9-8311 


9-7744 


13 


50 


10 20 


0-1794 


0-1211 


0-0628 


0-0056 


9-9484 


9-8913 


9-8342 


9-7765 


13 


40 


10 30 


01860 


0-1272 


0-0683 


0-0105 


9-9527 


9-8949 


9-8371 


9-7785 


13 


30 


10 40 


0-1926 


01332 


00738 


0-0154 


9-9570 


9-8985 


9-8400 


9-7805 


13 


20 


10 50 


0-1979 


0-1379 


0-0779 


0-0191 


9-9603 


9-9012 


9-8420 


9-7819 


13 


10 


11 


0-2032 


0-1426 


0-0820 


0-0228 


99636 


9-9038 


9-8440 


9-7834 


13 





11 10 


0-2070 


0-1462 


0-0853 


0-0257 


9-9661 


9-9061 


9-8461 


9-7849 


12 


50 


11 20 


0-2108 


0-1497 


0-0886 


0-0286 


9-9686 


9-9084 


9-8474 


9-7858 


12 


40 


11 30 


02126 


01513 


0-0899 


00299 


9-9698 


9-9090 


9-8479 


9-7861 


12 


30 


11 40 


02144 


0-1528 


0-0912 


0-0311 


9-9710 


9-9096 


9-8484 


9-7864 


12 


20 


11 50 


0-2154 


0-1538 


0-0922 


00318 


9-9713 


9-9101 


9-8490 


9-7867 


12 


10 


12 


0-2164 


0-1548 


0-0932 


0-0324 


9-9716 


9-9106 


98496 


9-7871 


12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOE, LAT. 55° 56'. 



293 







72° 


74° 


76° 


78° 


80° 


8 


2° 


84° 


86° 






H. 


M. 


































H. 


M. 


6 





65 c 


26' 


68 c 


52' 


70 c 


18' 


72 c 


57' 


75° 


36' 


78° 


25' 


81 c 


14' 


84° 


8' 


18 





6 


10 


63 


29 


66 


20 


68 


11 


70 


45 


73 


18 


76 


4 


78 


49 


81 


42 


17 


50 


6 


20 


61 


32 


63 


48 


66 


4 


68 


32 


71 





73 


42 


76 


24 


79 


15 


17 


40 


6 


30 


59 


38 


61 


48 


63 


57 


66 


22 


68 


46 


71 


24 


74 


1 


76 


44 


17 


30 


6 


40 


57 


44 


59 


47 


61 


50 


64 


11 


66 


32 


69 


5 


71 


38 


74 


13 


17 


20 


6 


50 


55 


48 


57 


49 


59 


49 


62 


4 


64 


18 


66 


47 


69 


16 


71 


53 


17 


10 


7 





53 


52 


55 


50 


57 


48 


59 


56 


62 


4 


64 


29 


66 


54 


69 


33 


17 





7 


10 


52 


3 


53 


55 


55 


46 


57 


20 


59 


54 


62 


14 


64 


34 


67 


9 


16 


50 


7 


20 


50 


14 


51 


59 


53 


44 


55 


44 


57 


44 


59 


59 


62 


14 


64 


45 


16 


40 


7 


30 


48 


23 


50 


3 


51 


42 


53 


38 


55 


33 


57 


43 


59 


53 


62 


32 


16 


30 


7 


40 


46 


32 


48 


7 


49 


42 


51 


32 


53 


21 


55 


27 


57 


32 


60 


18 


16 


20 


7 


50 


44 


43 


46 


14 


47 


44 


49 


30 


51 


15 


53 


16 


55 


17 


57 


47 


16 


10 


8 





42 


54 


44 


20 


45 


46 


47 


27 


49 


8 


51 


5 


53 


2 


55 


16 


16 





8 


10 


41 


4 


42 


27 


43 


49 


45 


29 


47 


8 


48 


57 


50 


46 


52 


56 


15 


50 


8 


20 


39 


14 


40 


33 


41 


52 


43 


30 


45 


8 


46 


49 


48 


30 


50 


35 


15 


40 


8 


30 


37 


26 


38 


41 


39 


55 


41 


26 


42 


56 


44 


35 


46 


14 


48 


14 


15 


30 


8 


40 


35 


38 


36 


48 


37 


58 


39 


21 


40 


44 


42 


21 


43 


58 


45 


53 


15 


20 


8 


50 


33 


50 


34 


57 


36 


3 


37 


22 


38 


40 


40 


11 


41 


42 


43 


34 


15 


10 


9 





32 


2 


33 


5 


34 


8 


35 


22 


36 


36 


38 


1 


39 


26 


41 


14 


15 





9 


10 


30 


16 


31 


15 


32 


13 


33 


23 


35 


33 


35 


54 


37 


15 


38 


56 


14 


50 


9 


20 


28 


30 


29 


24 


30 


18 


31 


24 


32 


30 


33 


47 


35 


4 


36 


38 


14 


40 


9 


30 


26 


44 


27 


38 


28 


32 


29 


29 


30 


26 


31 


38 


32 


49 


34 





14 


30 


9 


40 


24 


58 


25 


52 


26 


46 


27 


34 


28 


22 


29 


28 


30 


36 


31 


21 


14 


20 


9 


50 


23 


9 


23 


58 


24 


46 


25 


33 


26 


19 


27 


22 


28 


24 


29 


24 


14 


10 


10 





21 


20 


22 


3 


22 


46 


23 


31 


24 


16 


25 


15 


26 


14 


27 


26 


14 





10 


10 


19 


33 


20 


10 


20 


47 


21 


30 


22 


12 


23 


6 


24 





25 


7 


13 


50 


10 


20 


17 


46 


18 


17 


18 


48 


19 


28 


20 


8 


20 


57 


21 


46 


22 


47 


13 


40 


10 


30 


15 


58 


16 


27 


16 


56 


17 


33 


18 


9 


18 


53 


19 


37 


20 


32 


13 


30 


10 


40 


14 


10 


14 


37 


15 


4 


15 


37 


16 


10 


16 


49 


17 


28 


18 


16 


13 


20 


10 


50 


12 


25 


12 


46 


13 


7 


13 


38 


14 


9 


14 


42 


15 


14 


15 


59 


13 


10 


11 





10 


40 


10 


55 


11 


10 


11 


39 


12 


8 


12 


34 


13 





13 


41 


13 





11 


10 


8 


55 


9 


9 


9 


22 


9 


47 


10 


11 


10 


37 


11 


3 


11 


33 


12 


50 


11 


20 


7 


10 


7 


22 


7 


34 


7 


54 


8 


14 


8 


27 


8 


40 


9 


12 


12 


40 


11 


30 


5 


20 


5 


31 


5 


42 


5 


52 


6 


2 


6 


14 


6 


25 


6 


50 


12 


30 


11 


40 


3 


30 


3 


40 


3 


50 


3 


50 


3 


50 


4 





4 


10 


4 


28 


12 


20 


11 


50 


1 


45 


1 


50 


1 


55 


1 


55 


1 


55 


2 





2 


5 


2 


10 


12 


10 


12 





















































12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



294: 



LOG TAN-Z AND PAR. ANGLE (17) FOR LAT. 55° 56'. 




10 
20 



30 
40 
50 




10 
20 

30 
40 
50 



2 

2 10 

2 20 

2 30 

2 40 

2 50 




10 
20 

30 
40 
50 



4 

4 10 
4 20 



4 


30 


4 


40 


4 


50 




10 
20 

30 
40 
50 





Decl. 88° 
Log Tan 2 Z 



9-5938 
9-5938 
9-5940 

9-5945 
9-5950 
9-5955 

9-5960 
9-5966 
95972 

9-5986 
9-6000 
9-6015 

9-6030 
9-6047 
9-6064 

9-6085 
96106 
9-6125 

9-6144 
9-6167 
9-6190 

9-6215 
9-6240 
9-6265 

9-6290 
9-6315 
9-6340 

9-6374 
96408 
9-6423 

9-6438 
9-6471 
9-6504 

9-6531 
96558 
9-6588 

9-6618 



Decl. 88 c 
>? 



180° 0' 
177 30 
175 



172 
169 



102 
99 
97 



15 

30 



166 53 

164 16 

161 41 

159 6 



25 



156 

153 44 

151 5 

148 26 

145 50 

143 14 

140 37 

138 

135 24 

132 48 

130 14 

127 40 



125 4 

122 28 

119 55 

117 22 

114 49 

112 16 

109 43 

107 10 

104 38 



6 
35 

4 



94 33 
92 2 
89 32 



87 



24 
23 50 
23 40 



23 


30 


23 


20 


23 


10 


23 





22 


50 


22 


40 


22 


30 


22 


20 


22 


10 


22 





21 


50 


21 


40 


21 


30 


21 


20 


21 


10 


21 






21 





20 


50 


20 


40 


20 


30 


20 


20 


20 


10 


20 





19 


50 


19 


40 


19 


30 


19 


20 


19 


10 


19 





18 


50 


18 


40 


18 


30 


18 


20 


18 


10 


18 






H. M. 



6 

6 10 

6 20 

6 30 

6 40 

6 50 



11 
11 
11 

11 
11 
11 




10 
20 

30 
40 

50 


10 
20 



8 30 

8 40 

8 50 

9 
9 10 
9 20 

9 30 

9 40 

9 50 

10 

10 10 

10 20 

10 30 

10 40 

10 50 




10 
20 

30 
40 
50 



12 



Decl. 88° 
Log Tan 2 Z 



9-6618 
9-6645 
9-6672 

9-6700 
9-6728 
9-6757 

9-6786 
9-6813 
9-6840 

9-6862 
9-6884 
9-6910 

9-6936 
9-6961 
96986 

9-7007 
9-7028 
9-7049 

9-7070 
9-7088 
9-7106 

9-7123 
9-7140 
9-7152 

9-7164 
9-7176 

9-7188 

9-7199 
9-7210 
9-7219 

9-7228 
9-7237 
9-7242 

9-7242 
9-7244 
9-7244 

9-7246 



Decl. 88 c 



87° 2' 

84 34 

82 6 

79 27 

76 48 

74 30 

72 12 

69 44 

67 16 

64 49 

62 22 

59 56 

57 30 

55 5 

52 40 

50 14 

47 48 

45 25 

43 2 

40 37 

38 12 

35 49 

33 26 

31 2 

28 38 

26 13 

23 48 

21 26 

19 4 

16 43 



14 

12 

9 

7 
4 
9 



22 

3 

44 

5 
24 
12 



II 







15 
14 
14 







17 50 

17 40 

17 30 

17 20 

17 10 

17 

16 50 

16 40 

16 30 

16 20 

16 10 

16 

15 50 

15 40 

15 30 

15 20 

15 10 




50 
40 



14 30 

14 20 



1* 

14 





13 


50 


13 


40 


13 


30 


13 


20 


13 


10 


13 





12 


50 


12 


40 


12 


30 


12 


20 


12 


10 


12 






TABLE 



CONTAINING 



THE LOGARITHM OF TAN 2 ZENITH DISTANCE 



PARALLACTIC ANGLE 



FOR 



LATITUDE 57° 30', AND DECLINATION 40° to 90 c 



VOL. XXXIII. PART II. 2 U 



296 



LOGARITHM OF Tan 2 Z FOR LAT. 57° 30'. 





40° 


42° 


44° 


46° 


48° 


50° 


52° 


54° 






H. M. 


















H. 


M. 





8-9979 


8-8795 


8-7611 


8-6046 


8-4480 


8-2073 


7-9667 


7-4039 


24 





10 


90023 


8-8864 


8-7705 


8-6159 


8-4612 


8-2379 


8-0145 


7-5547 


23 


50 


20 


90136 


88993 


8-7849 


8-6376 


8-4904 


8-2823 


8-0743 


7-7754 


23 


40 


30 


90324 


8-9168 


8-8012 


8-6706 


8-5400 


8-3613 


8-1826 


7-9754 


23 


30 


40 


90570 


8-9529 


8-8488 


8-7229 


8-5969 


8-4437 


8-2916 


8-1437 


23 


20 


50 


9-0879 


8-9902 


8-8924 


8-7784 


8-6644 


8-5316 


8-3987 


8-2885 


23 


10 


1 


9-1225 


9-0319 


8-9393 


8-8362 


8-7330 


8-6226 


8-5121 


8-4223 


23 





1 10 


91607 


9-0758 


8-9909 


8-8973 


8-8042 


8-7086 


8-6129 


8-5384 


22 


50 


1 20 


9-2016 


9-1220 


9-0424 


8-9582 


8-8740 


8-7907 


8-7073 


8-6436 


22 


40 


1 30. 


9-2444 


9-1701 


9-0958 


9-0192 


8-9425 


8-8686 


8-7945 


8-7383 


22 


30 


1 40 


9-2881 


9-2189 


9-1496 


9-0792 


9-0087 


8-9425 


8-8763 


8-8258 


22 


20 


1 50 


9-3329 


9-2679 


92029 


9-1379 


9-0728 


9-0024 


8-9520 


8-9061 


22 


10 


2 


9-3775 


9-3154 


9-2552 


9-1949 


9-1345 


90790 


9-0234 


8-9799 


22 





2 10 


9-4227 


9-3649 


9-3069 


9-2505 


9-1939 


9-1422 


90903 


9-0495 


21 


50 


2 20 


9-4676 


9-4126 


9-3576 


9-3044 


9-2511 


9-2025 


9-1538 


9-1147 


21 


40 


2 30 


95123 


9-4598 


9-4071 


93566 


93059 


9-2610 


9-2159 


9-1723 


21 


30 


2 40 


9-5566 


9-5064 


9-4558 


9-4075 


9-3592 


93151 


9-2709 


9-2345 


21 


20 


2 50 


9-6008 


9-5522 


9-5036 


9-4573 


9-4109 


9-3623 


9-3247 


9-2890 


21 


10 


3 


9-6445 


9-5955 


9-5505 


9-5036 


9-4608 


9-4196 


9-3784 


93435 


21 





3 10 


9-6871 


9-6364 


9-5953 


9-5472 


9-5087 


9-4684 


9-4279 


9-3935 


20 


50 


3 20 


9-7298 


9-6850 


9-6402 


9-5976 


95550 


95156 


9-4761 


9-4421 


20 


40 


3 30 


9-7718 


9-7277 


9-6840 


9-6422 


9-6004 


9-5617 


9-5229 


9-4908 


20 


30 


3 40 


9-8138 


9-7705 


97271 


9-6860 


9-6448 


9-6066 


9-5683 


9-5344 


20 


20 


3 50 


9-8551 


98123 


97694 


9-7287 


9-6879 


9-6500 


9-6120 


9-5781 


20 


10 


4 


9-8962 


9-8536 


9-8111 


9-7706 


9-7301 


9-6923 


9-6546 


9-6205 


20 





4 10 


9-9369 


9-8946 


9-8522 


98119 


9-7716 


9-7339 


9-6961 


96619 


19 


50 


4 20 


9-9778 


99353 


9-8929 


9-8526 


9-8123 


9-7744 


9-7367 


9-7020 


19 


40 


4 30 


00184 


9-9757 


9-9331 


9-8927 


9-8522 


9-8142 


9-7762 


9-7412 


19 


30 


4 40 


0-0587 


00158 


9-9728 


9-9322 


9-8915 


98533 


9-8150 


9-7795 


19 


20 


4 50 


0-0988 


00554 


00122 


9-9712 


99301 


9-8916 


9-8529 


9-8171 


19 


10 


5 


0-1388 


00951 


00513 


00099 


9-9684 


9-9293 


9-8902 


9-8549 


19 





5 10 


0-1788 


01343 


0-0898 


0-0480 


00062 


9-9715 


9-9267 


9-8896 


18 


50 


5 20 


02190 


0-1736 


0-1282 


0-0858 


00434 


0-0031 


99628 


9-9249 


18 


40 


5 30 


0-2593 


02131 


0-1669 


01235 


00801 


00391 


99981 


9-9596 


18 


30 


5 40 


0-2994 


02525 


0-2055 


0-1612 


0-1169 


00750 


00332 


9-9938 


18 


20 


5 50 


0-3398 


02915 


0-2431 


0-1980 


0-1529 


01101 


00673 


0-0272 


18 


10 


6 


03805 


03311 


0-2817 


02354 


0-1890 


0-1453 


01016 


00604 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOR LAT. 57° 30'. 



29: 







40° 


4 


2° 


44° 


46° 


48' 


50° 


52° 


54° 






H. 


M. 
































H. 


M. 








0° 


0' 


0° 


0' 


0° 


0' 


0° 0' 


0° 


0' 


0° 


0' 


0° 


0' 


0° 


0' 


24 








10 


4 


34 


5 


12 


5 


50 


7 2 


8 


13 


11 


5 


13 


56 


26 


49 


23 


50 





20 


8 


54 


10 


7 


11 


20 


13 33 


15 


45 


20 


12 


25 


39 


42 


27 


23 


40 





30 


13 


1 


14 


48 


16 


34 


19 35 


22 


36 


28 


45 


34 


53 


50 


48 


23 


30 





40 


16 


55 


19 


8 


21 


20 


24 58 


28 


35 


35 


26 


42 


17 


56 


23 


23 


20 





50 


20 


37 


23 


8 


25 


38 


29 38 


33 


38 


40 


32 


47 


26 


59 


55 


23 


10 


1 





24 





26 


44 


29 


28 


33 41 


37 


53 


44 


42 


51 


31 


62 


27 


23 





1 


10 


27 


3 


29 


54 


32 


45 


36 48 


40 


40 


46 


45 


52 


49 


63 


19 


22 


50 


1 


20 


29 


45 


32 


42 


35 


39 


39 55 


44 


10 


50 


21 


56 


31 


65 


12 


22 


40 


1 


30 


32 


9 


35 


8 


38 


7 


42 19 


46 


30 


52 


15 


58 





65 


50 


22 


30 


1 


40 


34 


16 


37 


16 


40 


15 


44 15 


48 


15 


53 


42 


59 


8 


66 


14 


22 


20 


1 


50 


3(3 


7 


39 


3 


41 


58 


45 50 


49 


41 


54 


32 


59 


22 


66 


17 


22 


10 


2 





37 


44 


40 


48 


43 


27 


47 9 


50 


51 


55 


37 


60 


23 


66 


19 


22 





2 


10 


39 


7 


41 


54 


44 


39 


48 11 


51 


43 


56 


10 


60 


36 


66 


6 


21 


50 


2 


20 


40 


18 


42 


59 


45 


40 


49 2 


52 


23 


56 


34 


60 


45 


65 


49 


21 


40 


2 


30 


41 


17 


43 


52 


46 


26 


49 39 


52 


51 


56 


47 


60 


42 


65 


24 


21 


30 


2 


40 


42 


9 


44 


38 


47 


6 


50 38 


53 


10 


56 


52 


60 


33 


64 


56 


21 


20 


2 


50 


42 


52 


45 


17 


47 


41 


50 42 


53 


19 


56 


49 


60 


18 


64 


23 


21 


10 


3 





43 


25 


45 


45 


48 


5 


50 47 


53 


26 


56 


42 


59 


57 


63 


47 


21 





3 


10 


43 


49 


46 


1 


48 


13 


50 46 


53 


20 


56 


25 


59 


30 


63 


5 


20 


50 


3 


20 


44 


8 


46 


13 


48 


17 


50 45 


53 


13 


56 


7 


59 





62 


23 


20 


40 


3 


30 


44 


21 


46 


20 


48 


19 


50 38 


52 


56 


55 


41 


58 


26 


61 


11 


20 


30 


3 


40 


44 


29 


46 


23 


48 


16 


50 29 


52 


41 


55 


17 


57 


52 


60 


51 


20 


20 


3 


50 


44 


29 


46 


18 


48 


7 


50 12 


52 


16 


54 


45 


57 


14 


60 


3 


20 


10 


4 





44 


30 


46 


12 


47 


55 


49 55 


51 


54 


54 


13 


56 


32 


59 


12 


20 





4 


10 


44 


24 


46 


15 


47 


39 


49 33 


51 


26 


53 


37 


55 


48 


58 


19 


19 


50 


4 


20 


44 


14 


46 


17 


47 


19 


49 7 


50 


54 


52 


59 


55 


3 


57 


25 


19 


40 


4 


30 


44 


1 


45 


26 


46 


50 


48 35 


50 


19 


52 


17 


54 


15 


56 


30 


19 


30 


4 


40 


43 


44 


45 


7 


46 


30 


48 6 


49 


43 


51 


40 


53 


26 


55 


34 


19 


20 


4 


50 


43 


23 


44 


42 


46 





47 32 


49 


4 


50 


50 


52 


35 


54 


36 


19 


10 


5 





42 


59 


43 


59 


45 


29 


46 56 


48 


23 


50 


3 


51 


43 


53 


41 


19 





5 


10 


42 


33 


43 


44 


44 


55 


46 17 


47 


39 


49 


14 


50 


48 


52 


7 


18 


50 


5 


20 


44 


4 


43 


12 


44 


19 


45 37 


46 


51 


48 


22 


49 


53 


51 


36 


18 


40 


5 


30 


41 


32 


42 


36 


43 


39 


44 53 


46 


7 


47 


22 


48 


55 


50 


54 


18 


30 


5 


40 


40 


58 


41 


59 


42 


59 


44 9 


45 


18 


46 


38 


47 


58 


48 


30 


18 


20 


5 


50 


40 


23 


41 


20 


42 


15 


43 22 


44 


28 


45 


43 


46 


57 


48 


25 


18 


10 


6 





39 


44 


40 


38 


41 


31 


42 34 


43 


35 


44 


47 


45 


58 


47 


21 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



298 



LOGARITHM OF Tan 2 Z FOR LAT. 57° 30'. 



H. M. 



6 

6 10 
6 20 



11 
11 
11 



30 
40 



6 50 




10 

20 



7 30 

7 40 

7 50 

8 
8 10 

8 20 



8 30 

8 40 

8 50 

9 
9 10 
9 20 

9 30 

9 40 

9 50 

10 

10 10 

10 20 



10 30 
10 40 
10 50 




10 

20 



11 30 

11 40 

11 50 

12 



40° 



42° 



0-3805 
04217 
0-4627 

0-5039 
0-5458 
0-5879 

0-6305 
0-6729 
0-7163 

0-7603 
0-8045 
0-8489 

0-8942 
0-9393 
0-9855 

1-0312 
1-0784 
1-1250 

1-1722 
1-2184 
1-2648 

1-3112 
1-3574 
1-4020 

1-4472 
1-4898 
1-5314 

1-5690 
1-6064 
1-6386 

1-6702 

1-6952 
1-7192 

1-7362 
1-7506 
1-7572 

1-7612 



0-3311 
0-3708 
0-4103 

0-4498 
0-4900 
0-5299 

0-5703 
0-6104 
0-6512 

0-6925 
0-7336 
0-7749 

0-8167 
0-8581 
0-9004 

0-9420 
0-9847 
1-0266 

1-0688 
1-1099 
1-1509 

1-1916 
1-2320 
1-2705 

1-3094 
1-3460 
1-3809 

1-4131 
1-4439 
1-4712 

1-4972 
1-5183 
1-5377 

1-5518 
1-5633 
1-5688 

1-5721 



44 c 



0-2817 
0-3200 
0-3579 

03957 
0-4340 
0-4720 

0-5101 

0-5478 
0-5861 

0-6246 
0-6628 
0-7008 

0-7392 
0-7770 
0-8153 

0-8529 
0-8910 
0-9283 

0-9655 
1-0014 
1-0370 

1-0721 
1-1067 
1-1391 

1-1716 
1-2022 
1-2304 

1-2572 
1-2814 
1-3038 

1-3242 
1-3414 
1-3562 

1-3674 
1-3760 
1-3804 

1-3830 



46 c 



0-2354 
0-2724 
0-3091 

0-3455 
0-3822 
0-4185 

0-4549 
0-4908 
0-5270 

0-5633 
0-5993 
06350 

0-6708 
0-7060 
0-7414 

0-7761 
0-8111 
0-8453 

0-8792 
0-9117 
09439 

09754 
1-0056 
10352 

1-0642 
1-0910 
1-1160 

1-1392 
1-1608 
1-1798 

1-1977 
1-2127 
1-2254 

1-2353 
1-2426 
1-2462 

1-2485 



48° 



0-1890 
0-2249 
0-2603 

0-2952 
0-3304 
0-3651 

0-3998 
0-4338 
0-4680 

0-5020 
0-5359 
0-5691 

0-6024 
0-6349 
0-6676 

0-6993 
0-7313 
0-7622 

0-7928 
0-8221 
0-8507 

0-8787 
0-9059 
09313 

09568 
0-9798 
1-0016 

1-0212 
1-0402 
1-0558 

1-0712 
1-0840 
1-0946 

1-1032 
1-1092 
1-1120 

1-1140 



50 3 



52° 



01453 
0-1801 
0-2144 

0-2482 
0-2821 
03154 

0-3485 
0-3810 
0-4136 

0-4459 
0-4779 
0-5093 

0-5407 
0-5711 
0-6016 

0-6312 

0-6608 
0-6895 

0-7177 
0-7446 
0-7708 

0-7964 
0-8211 
0-8442 

0-8673 
0-8882 
0-9076 

0-9253 
0-9424 
0-9563 

0-9698 
09813 
0-9907 

0-9981 
1-0034 
1-0060 

1-0079 



0-1016 
0-1354 
0-1685 

0-2011 
02337 
0-2655 

0-2973 
0-3283 
0-3592 

0-3899 
0-4200 
0-4494 

0-4789 
0-5072 
05357 

0-5630 
0-5904 
0-6167 

0-6426 
0-6671 
0-6909 

0-7141 
0-7364 
0-7571 

0-7778 
0-7966 
0-8136 

0-8294 
0-8446 
0-8568 

0-8684 
0-8786 
0-8868 

08930 
0-8976 
0-9000 

0-9018 



54 c 



0-0604 
0-0932 
0-1252 

0-1567 
0-1881 
0-2188 

0-2493 

0-2789 
0-3084 

0-3376 
0-3662 
0-3941 

0-4219 

0-4487 
0-4754 

0-5010 
0-5267 
0-5512 

0-5754 
0-5980 
0-6201 

0-6414 
0-6620 
0-6810 

0-6998 
0-7169 
07329 

0-7470 
0-7606 
0-7717 

0-7826 
0-7917 
07993 

0-8048 
0-8091 
0-8110 

0-8126 



H. 


M. 


18 





17 


50 


17 


40 


17 


30 


17 


20 


17 


10 


17 





16 


50 


16 


40 


16 


30 


16 


20 


16 


10 


16 





15 


50 


15 


40 


15 


30 


15 


20 


15 


10 


15 





14 


50 


14 


40 


14 


30 


14 


20 


14 


10 


14 





13 


50 


13 


40 


13 


30 



13 20 

13 10 

13 

12 50 

12 40 



12 30 
12 20 
12 10 



12 



Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PAEALLACTIC ANGLE FOE LAT. 57° 30'. 



299 







40° 


42° 


44° 


46° 


48° 


50° 


52° 


54° 






H. 


M. 


















H. 


M. 


6 





39° 44' 


40° 38' 


41°31' 


42° 34' 


43° 35' 


44° 47' 


45° 58' 


47° 21' 


18 





6 


10 


39 4 


39 54 


40 44 


41 43 


42 41 


43 49 


44 56 


46 14 


17 


50 


6 


20 


38 21 


39 9 


39 56 


40 51 


41 46 


42 50 


43 54 


45 8 


17 


40 


6 


30 


37 37 


38 22 


39 6 


39 58 


40 50 


41 50 


42 50 


44 


17 


30 


6 


40 


36 50 


37 33 


38 14 


39 3 


39 51 


40 48 


41 45 


42 51 


17 


20 


6 


50 


36 2 


36 41 


37 20 


38 6 


38 52 


39 46 


40 39 


41 41 


17 


10 


7 





35 12 


35 49 


36 25 


37 8 


37 51 


38 41 


39 31 


40 30 


17 





7 


10 


34 20 


34 55 


35 29 


36 9 


36 49 


37 37 


38 24 


39 20 


16 


50 


7 


20 


33 27 


33 59 


34 30 


35 8 


35 46 


36 30 


37 14 


38 7 


16 


40 


7 


30 


32 32 


33 2 


33 31 


34 6 


34 41 


35 23 


36 4 


36 53 


16 


30 


7 


40 


31 35 


32 3 


32 30 


33 3 


33 36 


34 15 


34 53 


35 39 


J6 


20 


7 


50 


30 36 


31 2 


31 27 


31 58 


32 29 


33 5 


33 41 


34 25 


16 


10 


8 





29 36 


30 


30 23 


30 52 


31 20 


31 55 


32 29 


33 9 


16 





8 


10 


28 35 


28 57 


29 18 


29 45 


30 11 


30 43 


31 15 


31 53 


15 


50 


8 


20 


27 32 


27 52 


28 12 


28 37 


29 1 


29 31 


30 


30 36 


15 


40 


8 


30 


26 28 


26 46 


27 5 


27 27 


27 50 


28 18 


28 45 


29 18 


15 


30 


8 


40 


25 22 


25 39 


25 55 


26 17 


26 37 


27 3 


27 29 


28 


15 


20 


8 


50 


24 15 


24 30 


24 46 


25 5 


25 24 


25 48 


26 12 


26 40 


15 


10 


9 





23 8 


23 22 


23 36 


23 54 


24 11 


24 33 


24 55 


25 22 


15 





9 


10 


21 57 


22 10 


22 22 


22 39 


22 55 


23 15 


23 35 


24 


14 


50 


9 


20 


20 46 


20 58 


21 9 


21 24 


21 39 


21 58 


22 16 


22 39 


14 


40 


9 


30 


19 34 


19 45 


19 55 


20 8 


20 22 


20 39 


20 56 


21 17 


14 


30 


9 


40 


18 21 


18 31 


18 40 


18 52 


19 4 


19 20 


19 35 


19 55 


14 


20 


9 


50 


17 8 


17 16 


17 24 


17 35 


17 46 


18 


18 14 


18 32 


14 


10 


10 





15 53 


16 


16 4 


16 17 


16 28 


16 41 


16 54 


17 7 


14 





10 


10 


14 38 


14 45 


14 52 


15 


15 8 


15 21 


15 34 


15 30 


13 


50 


10 


20 


13 24 


13 24 


13 24 


13 34 


13 44 


13 54 


14 4 


14 21 


13 


40 


10 


30 


12 4 


12 11 


12 18 


12 20 


12 22 


12 33 


12 44 


12 54 


13 


30 


10 


40 


10 50 


10 44 


10 38 


10 50 


11 2 


11 14 


11 26 


11 30 


13 


20 


10 


50 


9 16 


9 23 


9 30 


9 30 


9 30 


9 42 


9 54 


9 58 


13 


10 


11 





8 8 


8 5 


8 2 


8 8 


8 14 


8 17 


8 20 


8 33 


13 





11 


10 


6 22 


6 36 


6 50 


6 57 


7 4 


7 10 


7 16 


7 22 


12 


50 


11 


20 


5 30 


5 21 


5 12 


5 17 


5 22 


5 30 


5 38 


5 50 


12 


40 


11 


30 


3 54 


3 59 


4 4 


4 20 


4 30 


4 20 


4 16 


4 30 


12 


30 


11 


40 


2 44 


2 26 


2 8 


2 26 


2 44 


2 36 


2 28 


2 52 


12 


20 


11 


50 


1 22 


1 13 


1 4 


1 13 


1 22 


1 18 


1 14 


1 26 


12 


10 


12 





























12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



300 



LOGARITHM OF Tan 2 Z FOR LAT. 57° 30'. 







56° 


58° 


60° 


62° 


64° 


66° 


68° 


70° 






H. 


M. 


















H. 


II. 


o 


o 


68410 
7-0948 
7-4766 




7-2762 
7-4268 
7-5986 


7-6946 
7-7791 

7-8831 


8-1129 
8-1314 
8-1699 


8-3244 
8-3363 
8-3624 


8-5357 
85411 
8-5552 


8-6802 


24 


o 


o 


10 




8-6842 
8-6945 


23 

23 


50 
40 





20 


7-2220 





30 


7-7683 


7-5400 


7-8141 


8-0247 


8-2352 


8-4075 


8-5799 


8-7121 


23 


30 





40 


7-9958 


7-8580 


8-0059 


8-1563 


8-3068 


8-4586 


8-6104 


8-7346 


23 


20 





50 


8-1783 


8-1731 


8-1679 


8-2787 


8-3893 


8-5185 


8-6476 


8-7577 


23 


10 


1 





83324 


8-3222 


8-3120 


8-3911 


8-4702 


8-5796 


8-6889 


8-7944 


23 





1 


10 


8-4639 


8-4495 


8-4351 


8-4932 


8-5511 


8-6427 


8-7341 


8-8294 


22 


50 


1 


20 


8-5798 


8-5630 


8-5462 


8-5876 


8-6289 


8-7047 


8-7804 


8-8656 


22 


40 


1 


30 


8-6819 


8-6633 


8-6445 


8-6740 


8-7033 


8-7658 


8-8282 


8-9037 


22 


30 


1 


40- 


8-7743 


8-7549 


8-7353 


8-7554 


8-7643 


8-8249 


8-8758 


8-9420 


22 


20 


1 


50 


8-8601 


8-8386 


8-8169 


8-8246 


8-8321 


8-8777 


8-9232 


8-9811 


22 


10 


2 





8-9365 


8-9146 


8-8928 


8-8992 


8-9057 


8-9381 


8-9705 


90205 


22 





2 


10 


9-0085 


8-9858 


8-9629 


8-9634 


8-9637 


8-9904 


9-0169 


9-0547 


21 


50 


2 


20 


90756 


9-0524 


90291 


9-0267 


90241 


9-0432 


9-0621 


9-0982 


21 


40 


2 


30 


9-1385 


9-1145 


9-0904 


9-0847 


9-0790 


9-0875 


9-1055 


9-1362 


21 


30 


2 


40 


9-1979 


9-1735 


9-1489 


91363 


9-1317 


9-1363 


9-1489 


9-1737 


21 


20 


2 


50 


92544 


9-2295 


9-2045 


9-1935 


9-1824 


9-1808 


9-1906 


9-2046 


21 


10 


3 





9-3086 


9-2829 


9-2572 


92439 


9-2306 


9-2315 


9-2323 


9-2473 


21 





3 


10 


9-3589 


9-3328 


9-3066 


9-2914 


9-2761 


9-2732 


9-2701 


92816 


20 


50 


3 


20 


9-4080 


9-3811 


9-3543 


93372 


9-3202 


9-3148 


9-3095 


9-3164 


20 


40 


3 


30 


9-4585 


9-4294 


9-4002 


9-3815 


9-3627 


9-3548 


9-3468 


9-3501 


20 


30 


3 


40 


9-5004 


9-4724 


9-4443 


9-4243 


9-4041 


9-3936 


9-3831 


93832 


20 


20 


3 


50 


9-5441 


95155 


9-4867 


9-4653 


9-4438 


9-4310 


9-4181 


9-4154 


20 


10 


4 





9-5864 


9-5572 


9-5279 


9-5051 


9-4822 


9-4674 


9-4526 


9-4470 


20 





4 


10 


9-6275 


9-5970 


9-5676 


9-5436 


9-5196 


9-5029 


9-4862 


9-4779 


19 


50 


4 


20 


9-6674 


9-6368 


9-6062 


9-5810 


9-5558 


9-5372 


9-5186 


9-5079 


19 


40 


4 


30 


97063 


9-6745 


9-6437 


9-6174 


9-5909 


9-5704 


95499 


9-5373 


19 


30 


4 


40 


97440 


9-7121 


9-6802 


9-6527 


9-6251 


9-6032 


9-5812 


9-5660 


19 


20 


4 


50 


9-7811 


9-7485 


9-7156 


9-6871 


9-6585 


9-6349 


9-6112 


9-5940 


19 


10 


5 





98196 


9-7849 


9-7502 


9-7204 


9-6906 


9-6657 


9-6407 


9-6214 


19 





5 


10 


9-8525 


9-8185 


9-7838 


9-7524 


9-7210 


9-6952 


9-6693 


9-6481 


18 


50 


5 


20 


9-8871 


9-8520 


9-8169 


9-7851 


97532 


9-7253 


9-6974 


9-6744 


18 


40 


5 


30 


9-9211 


9-8848 


9-8488 


9-8160 


9-7831 


9-7538 


9-7244 


9-6997 


18 


30 


5 


40 


99543 


9-9175 


9-8806 


9-8466 


9-8126 


9-7820 


9-7514 


97250 


18 


20 


5 


50 


99871 


9-9490 


9-9114 


98762 


9-8410 


9-8091 


9-7773 


9-7492 


18 


10 


6 





0-0192 


9-9804 


9-9416 


9-9054 


9-8693 


9-8383 


9-8074 


9-7755 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANCLE FOR LAT. 57° 30'. 



301 







56° 


58° 


60° 


62° 


64° 


66° 


68° 


70° 






H. 


M. 


















H. 


M. 








0° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


180° 0' 


24 








10 


39 41 


109 28 


152 20 


160 25 


168 30 


170 32 


172 34 


173 35 


23 


50 





20 


59 15 


98 28 


131 39 


144 23 


157 6 


161 14 


165 23 


167 20 


23 


40 





30 


66 42 


94 46 


120 12 


133 52 


147 31 


152 58 


158 25 


161 13 


23 


30 





40 


70 29 


91 4 


111 19 


124 58 


138 36 


145 14 


151 52 


155 23 


23 


20 





50 


72 23 


89 7 


105 51 


117 59 


130 7 


138 23 


145 40 


149 49 


23 


10 


1 





73 23 


87 10 


101 14 


113 1 


124 47 


132 20 


139 54 


144 31 


23 





1 


10 


73 48 


85 40 


97 48 


108 54 


120 


127 17 


134 34 


139 31 


22 


50 


1 


20 


73 52 


84 8 


94 48 


104 40 


114 33 


122 4 


129 36 


134 50 


22 


40 


1 


30 


73 40 


82 49 


92 23 


101 25 


110 26 


117 44 


125 3 


130 25 


22 


30 


1 


40 


73 19 


81 30 


89 58 


98 18 


106 38 


113 43 


120 49 


126 16 


22 


20 


1 


50 


72 51 


80 20 


88 3 


95 40 


103 19 


110 7 


116 55 


122 7 


22 


10 


2 





72 15 


79 7 


85 59 


93 5 


100 10 


106 42 


113 15 


118 40 


22 





2 


10 


71 36 


77 54 


84 12 


90 48 


97 24 


103 37 


109 51 


115 12 


21 


50 


2 


20 


70 52 


76 41 


82 29 


88 38 


94 46 


100 41 


106 37 


111 54 


21 


40 


2 


30 


70 6 


75 13 


80 20 


86 20 


92 19 


97 58 


103 37 


108 45 


21 


30 


2 


40 


69 18 


74 18 


79 17 


84 40 


90 1 


95 23 


100 46 


105 45 


21 


20 


2 


50 


68 28 


73 7 


77 46 


82 50 


87 53 


92 58 


98 3 


102 53 


21 


10 


3 





67 36 


71 57 


76 17 


81 


85 44 


90 35 


95 26 


100 7 


21 





3 


10 


66 40 


70 45 


74 50 


79 17 


83 44 


88 20 


92 57 


97 27 


20 


50 


3 


20 


65 45 


69 35 


73 24 


77 36 


81 47 


86 11 


90 35 


94 58 


20 


40 


3 


30 


64 55 


68 27 


71 59 


75 77 


79 55 


84 8 


88 20 


92 28 


20 


30 


3 


40 


63 50 


67 14 


70 37 


74 21 


78 5 


82 53 


86 4 


90 26 


20 


20 


3 


50 


62 51 


66 3 


69 15 


72 47 


76 19 


80 7 


83 55 


87 51 


20 


10 


4 





61 51 


64 52 


67 53 


71 14 


74 35 


78 12 


81 49 


85 36 


20 





4 


10 


60 50 


63 41 


66 32 


69 43 


72 53 


78 20 


79 46 


83 24 


19 


50 


4 


20 


59 46 


62 29 


65 11 


68 12 


71 12 


74 30 


77 47 


81 16 


19 


40 


4 


30 


58 45 


61 18 


63 51 


66 42 


69 33 


72 42 


75 50 


79 11 


19 


30 


4 


40 


57 41 


60 6 


62 31 


65 14 


67 56 


70 56 


73 55 


77 8 


19 


20 


4 


50 


56 37 


58 24 


61 11 


63 46 


66 20 


69 11 


72 2 


75 7 


19 


10 


5 





55 38 


57 15 


59 51 


62 18 


64 45 


67 28 


70 11 


73 9 


19 





5 


10 


54 25 


56 29 


58 32 


60 51 


63 10 


65 46 


68 22 


71 13 


18 


50 


5 


20 


53 18 


55 15 


57 12 


59 25 


61 37 


64 5 


66 33 


69 17 


18 


40 


5 


30 


52 11 


54 2 


55 52 


57 58 


60 4 


62 27 


64 46 


67 23 


18 


30 


5 


40 


51 2 


52 48 


54 33 


56 32 


58 31 


60 48 


63 1 


65 31 


18 


20 


5 


50 


49 53 


51 33 


53 13 


55 7 


57 


59 9 


61 17 


63 44 


18 


10 


6 





48 43 


50 18 


51 52 


53 40 


55 28 


57 36 


59 43 


61 55 


18 






Horizontal Argument, Decimation. — Vertical Argument, Hour Angle. 



302 



LOGARITHM OF TAN 2 Z FOR LAT. 57° 30'. 







56° 


58° 


60° 


62° 


64° 


66° 


68° 


70° 






H. 


M. 


















H. 


M. 


6 





00192 


9-9804 


99416 


9-9054 


98693 


9-8383 


9-8074 


9-7755 


18 





6 


10 


00510 


00112 


9-9712 


9-9340 


9-8968 


9-8623 


9-8278 


9-7966 


17 


50 


6 


20 


0-0820 


0-0411 


0-0002 


9-9618 


9-9234 


9-8877 


9-8519 


9-8195 


17 


40 


6 


30 


0-1123 


0-0714 


00285 


9-9890 


9-9494 


9-9125 


9-8755 


9-8413 


17 


30 


6 


40 


01425 


0-0995 


0-0565 


00158 


9-9752 


9-9369 


9-8986 


9-8631 


17 


20 


6 


50 


01721 


0-1279 


0-0836 


0-0418 


o-oooo 


9-9605 


9-9220 


9-8841 


17 


10 


7 





02012 


0-1558 


0-1104 


0-0674 


0-0244 


9-9837 


99430 


9-9057 


17 





7 


10 


0-2295 


0-1829 


0-1363 


0-0921 


0-0479 


0-0060 


9-9640 


9-9244 


16 


50 


7 


20 


0-2576 


0-2098 


01619 


0-1165 


0-0711 


0-0280 


9-9848 


9-9438 


16 


40 


7 


30. 


0-2854 


0-2362 


0-1871 


0-1405 


00939 


0-0496 


0-0051 


9-9629 


16 


30 


7 


40 


0-3123 


0-2620 


0-2115 


0-1637 


0-1159 


0-0703 


0-0247 


9-9812 


16 


20- 


7 


50 


0-3388 


0-2870 


0-2352 


0-1862 


0-1371 


00903 


0-0436 


9-9988 


16 


10 


8 





03650 


03118 


0-2586 


0-2083 


0-1580 


0-1138 


00696 


00199 


16 





8 


10 


0-3902 


0-3356 


0-2810 


0-2295 


0-1779 


0-1288 


0-0797 


0-0325 


15 


50 


8 


20 


0-4152 


03592 


0-3032 


0-2504 


0-1976 


0-1473 


0-0970 


0-0487 


15 


40 


8 


30 


04391 


0-3817 


03243 


0-2703 


0-2162 


0-1648 


0-1133 


0-0639 


15 


30 


8 


40 


0-4630 


0-4041 


0-3452 


0-2900 


0-2347 


0-1822 


0-1296 


0-0790 


15 


20 


8 


50 


0-4857 


04254 


03651 


0-3087 


0-2522 


0-1985 


0-1448 


0-0932 


15 


10 


9 





0-5081 


0-4464 


03846 


0-3269 


02693 


0-2145 


0-1597 


0-1071 


15 





9 


10 


0-5289 


0-4658 


0-4027 


0-3438 


0-2849 


0-2291 


0-1732 


0-1196 


14 


50 


9 


20 


0-5492 


0-4846 


0-4201 


0-3601 


0-3000 


0-2432 


0-1864 


0-1327 


14 


40 


9 


30 


0-5687 


0-5028 


0-4369 


0-3757 


0-3145 


0-2568 


01990 


0-1434 


14 


30 


9 


40 


0-5875 


0-5203 


0-4530 


0-3907 


0-3284 


0-2696 


0-2108 


0-1544 


14 


20 


9 


50 


06049 


05363 


0-4677 


0-4044 


0-3411 


0-2814 


0-2217 


0-1644 


14 


10 


10 





0-6218 


0-5533 


0-4848 


04191 


0-3534 


02929 


02324 


0-1745 


14 





10 


10 


0-6372 


0-5663 


0-4954 


0-4299 


0-3644 


0-3031 


0-2418 


0-1830 


13 


50 


10 


20 


0-6522 


0-5797 


05072 


0-4411 


03750 


03130 


0-2510 


01914 


13 


40 


10 


30 


0-6646 


05914 


0-5182 


0-4510 


0-3838 


0-3211 


0-2584 


0-1982 


13 


30 


10 


40 


0-6766 


0-6026 


0-5286 


0-4607 


0-3928 


0-3293 


0-2658 


02052 


13 


20 


10 


50 


0-6866 


0-6117 


0-5368 


0-4684 


0-4000 


0-3358 


0-2716 


0-2105 


13 


10 


11 





06968 


0-6208 


0-5448 


0-4758 


0-4068 


0-3421 


0-2774 


0-2159 


13 





11 


10 


0-7048 


0-6282 


0-5516 


0-4820 


0-4124 


0-3473 


0-2822 


0-2204 


12 


50 


11 


20 


07118 


06345 


0-5572 


0-4870 


0-4168 


0-3517 


0-2866 


02241 


12 


40 


11 


30 


07166 


0-6389 


05612 


04907 


0-4202 


03547 


0-2892 


0-2268 


12 


30 


11 


40 


0-7206 


06426 


05646 


0-4940 


04234 


0-3576 


0-2918 


0-2292 


12 


20 


11 


50 


0-7220 


06441 


05662 


0-4954 


0-4246 


0-3587 


0-2928 


0-2301 


12 


10 


12 





07234 


06452 


0-5670 


0-4962 


04254 


0-3594 


02934 


02306 


12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOU LAT. 57° 30'. 



303 







56° 


58° 


60° 


6 


2° 


64° 


66° 


68° 


70° 






H. 


M. 


































H. 


M. 


6 





48 c 


43' 


50 c 


18' 


51 c 


52' 


53 c 


40' 


55 c 


28' 


57 c 


36' 


59 c 


43' 


61 c 


55' 


18 





6 


10 


47 


32 


49 


2 


50 


32 


52 


14 


53 


56 


55 


53 


57 


49 


60 


1 


17 


50 


6 


20 


46 


21 


47 


16 


49 


11 


50 


48 


52 


25 


54 


16 


56 


7 


58 


13 


17 


40 


6 


30 


45 


9 


46 


30 


47 


50 


49 


22 


50 


54 


52 


40 


54 


26 


56 


26 


17 


30 


6 


40 


43 


56 


45 


12 


46 


28 


47 


56 


49 


23 


51 


4 


52 


44 


54 


39 


17 


20 


6 


50 


42 


43 


43 


55 


45 


7 


46 


30 


47 


53 


49 


28 


51 


4 


52 


53 


17 


10 


7 





41 


29 


42 


37 


43 


44 


45 


3 


46 


22 


47 


53 


49 


23 


51 


8 


17 





7 


10 


40 


15 


41 


19 


42 


23 


43 


38 


44 


52 


46 


18 


47 


44 


49 


24 


16 


50 


7 


20 


38 


59 


39 


59 


41 





42 


10 


43 


21 


44 


43 


46 


4 


47 


39 


16 


40 


7 


30 


37 


42 


38 


39 


39 


36 


40 


43 


41 


50 


43 


7 


44 


25 


45 


55 


16 


30 


7 


40 


36 


25 


37 


19 


38 


13 


39 


16 


40 


19 


41 


33 


42 


46 


44 


12 


16 


20 


7 


50 


35 


8 


35 


59 


36 


49 


37 


49 


38 


48 


39 


58 


41 


7 


42 


29 


16 


10 


8 





33 


49 


34 


37 


35 


25 


36 


21 


37 


17 


38 


40 


40 


3 


41 


3 


16 





8 


10 


32 


30 


33 


16 


34 





34 


53 


35 


46 


36 


48 


37 


50 


39 


3 


15 


50 


8 


20 


31 


11 


31 


53 


32 


35 


33 


25 


34 


14 


35 


13 


36 


11 


37 


20 


15 


40 


8 


30 


29 


51 


30 


31 


31 


10 


31 


56 


32 


43 


33 


38 


34 


33 


35 


38 


15 


30 


8 


40 


28 


30 


29 


7 


29 


43 


30 


27 


31 


11 


32 


1 


32 


50 


33 


53 


15 


20 


8 


50 


27 


9 


27 


28 


28 


17 


28 


58 


29 


38 


30 


27 


31 


15 


32 


13 


15 


10 


9 





25 


48 


26 


20 


26 


52 


27 


30 


28 


8 


28 


53 


29 


38 


30 


33 


15 





9 


10 


24 


24 


24 


54 


25 


24 


26 





26 


35 


27 


17 


27 


59 


28 


50 


14 


50 


9 


20 


23 


1 


23 


29 


23 


56 


24 


29 


25 


2 


25 


42 


26 


21 


27 


8 


14 


40 


9 


30 


21 


38 


22 


3 


22 


28 


22 


59 


23 


29 


24 


6 


24 


43 


25 


26 


14 


30 


9 


40 


20 


14 


20 


37 


21 





21 


28 


21 


56 


22 


30 


23 


3 


23 


44 


14 


20 


9 


50 


18 


49 


19 


11 


19 


32 


19 


58 


20 


23 


20 


54 


21 


25 


22 


2 


14 


10 


10 





17 


20 


17 


57 


18 


34 


18 


41 


18 


48 


19 


17 


19 


46 


20 


21 


14 





10 


10 


15 


56 


16 


15 


16 


34 


16 


53 


17 


12 


17 


40 


18 


8 


18 


38 


13 


50 


10 


20 


14 


38 


14 


48 


14 


58 


15 


20 


15 


42 


16 


6 


16 


30 


16 


56 


13 


40 


10 


30 


13 


4 


13 


19 


13 


34 


13 


49 


14 


4 


14 


27 


14 


50 


15 


13 


13 


30 


10 


40 


11 


34 


11 


51 


12 


8 


12 


21 


12 


36 


12 


54 


13 


12 


13 


34 


13 


20 


10 


50 


10 


2 


10 


1? 


10 


32 


10 


47 


11 


2 


11 


14 


11 


26 


11 


47 


13 


10 


11 





8 


46 


8 


53 


9 





9 


15 


9 


30 


9 


37 


9 


44 


10 


4 


13 





11 


10 


7 


28 


7 


34 


7 


40 


7 


51 


8 


2 


8 


8 


8 


14 


8 


32 


12 


50 


11 


20 


6 


2 


6 


2 


6 


2 


6 


5 


6 


8 


6 


26 


6 


44 


6 


47 


12 


40 


11 


30 


4 


46 


4 


41 


4 


36 


4 


36 


4 


36 


4 


45 


4 


54 


5 


8 


12 


30 


11 


40 


3 


16 


3 


8 


3 





3 


8 


3 


16 


3 


22 


3 


28 


3 


35 


12 


20 


11 


50 


1 


38 


1 


34 


1 


30 


1 


34 


1 


38 


1 


41 


1 


44 


1 


48 


12 


10 


12 





















































12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 
VOL. XXXIII. PART II. 



2X 



304 



LOGARITHM OF TAN 2 Z FOR LAT. 57° 3()'. 







72° 


74° 


76° 


78° 


80° 


82° 


84° 


86° 






H. 


M. 


















H. 


M. 








8-8246 


8-9365 


9-0485 


9-1413 


92342 


9-3148 


9-3954 


9-4678 


24 








10 


8-8272 


8-9385 


9-0497 


9-1422 


9-2346 


9-3150 


9-3954 


9-4678 


23 


50 





20 


8-8338 


8-9435 


90531 


9-1448 


9-2364 


93162 


9-3962 


9-4683 


23 


40 





30 


8-8443 


89516 


9-0587 


9-1491 


9-2393 


9-3184 


9-3974 


9-4689 


23 


30 





40 


8-8588 


8-9625 


9-0663 


9-1547 


9-2431 


9-3212 


9-3992 


9-4703 


23 


20 





50 


8-8792 


8-9780 


9-0768 


9-1625 


9-2482 


9-3247 


9-4012 


9-4712 


23 


10 


1 





8-8998 


8-9936 


9-0874 


9-1709 


9-2543 


9-3297 


9-4042 


9-4735 


23 





1 


10 


8-9245 


9-0127 


9-1007 


9-1811 


9-2614 


9-3344 


9-4074 


9-4752 


22 


50 


1 


20 


8-9508 


90331 


9-1154 


9-1923 


9-2692 


9-3405 


9-4118 


9-4780 


22 


40 


1 


30 


8-9791 


9-0554 


9-1315 


9-2048 


9-2780 


9-3471 


9-4162 


9-4810 


22 


30 


1 


40 


9-0083 


9-0786 


9-1489 


9-2183 


9-2876 


9-3541 


9-4206 


9-4839 


22 


20 


1 


50 


9-0390 


9-1034 


9-1678 


92330 


9-2981 


9-3619 


9-4256 


9-4871 


22 


10 


2 





9-0604 


9-1288 


9-1872 


9-2482 


9-3092 


9-3702 


9-4312 


9-4906 


22 





2 


10 


9-0924 


9-1499 


9-2073 


9-2642 


9-3209 


9-3788 


9-4366 


9-4939 


21 


50 


2 


20 


91343 


9-1811 


9-2280 


9-2807 


9-3334 


9-3883 


9-4434 


9-4985 


21 


40 


2 


30 


9-1663 


9-2079 


9-2494 


9-2980 


9-3465 


9-3984 


9-4502 


9-5026 


21 


30 


2 


40 


9-1983 


9-2349 


9-2712 


9-3154 


93595 


9-4082 


9-4568 


9-5070 


21 


20 


2 


50 


9-2300 


9-2619 


9-2937 


9-3332 


9-3725 


9-4188 


9-4634 


9-5115 


21 


10 


3 





9-2622 


9-2892 


9-3163 


9-3521 


9-3880 


9-4297 


9-4704 


9-5165 


21 





3 


10 


9-2929 


9-3157 


9-3384 


9-3702 


9-4019 


9-4406 


9-4780 


9-5200 


20 


50 


3 


20 


9-3234 


9-3419 


9-3605 


9-3883 


9-4161 


9-4510 


9-4858 


9-5260 


20 


40 


3 


30 


9-3534 


9-3682 


9-3827 


9-4070 


9-4311 


9-4623 


9-4934 


9-5306 


20 


30 


3 


40 


93834 


9-3943 


9-4051 


9-4256 


9-4461 


9-4739 


9-5018 


9-5362 


20 


20 


3 


50 


9-4125 


9-4200 


9-4274 


9-4443 


9-4611 


9-4862 


9-5112 


9-5421 


20 


10 


4 





94414 


9-4454 


9-4494 


9-4628 


9-4761 


9-4981 


9-5200 


9-5479 


20 





4 


10 


9-4696 


9-4704 


9-4712 


9-4813 


9-4913 


9-5096 


9-5278 


9-5529 


19 


50 


4 


20 


9-4971 


9-4951 


9-4930 


9-4997 


9-5065 


9-5215 


9-5366 


9-5587 


19 


40 


4 


30 


9-5242 


9-5193 


9-5144 


9-5180 


9-5216 


9-5333 


9-5450 


9-5643 


19 


30 


4 


40 


9-5508 


9-5431 


9-5355 


9-5361 


9-5367 


9-5455 


9-5542 


9-5704 


19 


20 


4 


50 


9-5768 


9-5666 


9-5564 


9-5541 


9-5517 


9-5572 


9-5631 


9-5761 


19 


10 


5 





9-6020 


9-5894 


9-5768 


9-5717 


9-5666 


9-5693 


9-5720 


9-5822 


19 





5 


10 


9-6268 


96120 


9-5971 


9-5893 


9-5813 


9-5810 


9-5804 


9-5878 


18 


50 


5 


20 


9-6514 


9-6342 


9-6170 


9-6065 


9-5960 


9-5930 


9-5900 


9-5940 


18 


40 


5 


30 


9-6750 


96557 


96363 


9-6234 


9-6104 


9-6041 


9-5978 


9-5994 


18 


30 


5 


40 


9-6985 


9-6771 


9-6556 


9-6402 


9-6247 


9-6159 


9-6072 


9-6058 


18 


20 


5 


50 


9-7212 


9-6977 


96743 


9-6558 


96374 


9-6268 


9-6162 


9-6117 


18 


10 


6 





9-7435 


9-7182 


96929 


96727 


9-6526 


9-6384 


9-6242 


9-6171 

! 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOR LAT. 57° 30'. 



305 







7 


2° 


74° 


7 


6° 


7 


3° 


80° 


8 


2° 


84° 


86° 






H. 


M. 
































H. 


M. 








180° 


0' 


180° 


0' 


180° 


0' 


180° 


0' 


180° 0' 


180° 


0' 


180° 


0' 


180° 


0' 


24 








10 


174 


36 


175 


10 


175 


44 


176 


8 


176 32 


176 


46 


177 





177 


26 


23 


50 





20 


169 


17 


170 


24 


171 


31 


172 


17 


173 3 


173 


35 


174 


6 


174 


27 


23 


40 





30 


164 


2 


165 


41 


167 


20 


168 


25 


169 31 


170 


16 


171 





171 


34 


23 


30 





40 


158 


55 


161 


4 


163 


13 


164 


37 


166 1 


167 


3 


168 


4 


168 


46 


23 


20 





50 


153 


58 


156 


33 


159 


8 


160 


50 


162 33 


163 


48 


165 


2 


165 


57 


23 


10 


1 





149 


9 


152 


7 


155 


6 


157 


6 


159 6 


160 


33 


162 





163 


8 


23 





1 


10 


144 


29 


147 


48 


151 


8 


153 


25 


155 42 


157 


21 


159 





160 


18 


22 


50 


1 


20 


140 


4 


143 


40 


147 


16 


149 


48 


152 20 


154 


11 


156 


2 


157 


24 


21 


40 


1 


30 


135 


48 


139 


39 


143 


30 


147 


15 


149 1 


151 





153 





154 


35 


22 


30 


1 


40 


131 


43 


135 


45 


139 


57 


142 


15 


145 43 


147 


57 


150 


10 


151 


52 


22 


20 


1 


50 


127 


19 


131 


42 


136 


5 


138 


31 


142 28 


144 


51 


147 


14 


149 


5 


22 


10 


2 





124 


5 


128 


18 


132 


32 


135 


53 


139 14 


141 


47 


144 


20 


146 


19 


22 





2 


10 


120 


34 


124 


52 


129 


11 


132 


37 


136 4 


138 


45 


141 


26 


143 


34 


21 


50 


2 


20 


117 


11 


121 


32 


125 


53 


129 


25 


132 57 


135 


45 


138 


32 


140 


47 


21 


40 


2 


30 


113 


54 


117 


46 


122 


38 


126 


15 


129 53 


132 


47 


135 


40 


138 


4 


21 


30 


2 


40 


110 


44 


115 


6 


119 


28 


123 


9 


126 51 


129 


53 


132 


54 


135 


22 


21 


20 


2 


50 


107 


44 


112 


3 


116 


23 


120 


6 


123 50 


126 


58 


130 


6 


132 


40 


21 


10 


3 





104 


49 


108 


6 


113 


24 


117 


9 


120 54 


124 


6 


127 


18 


129 


59 


21 





3 


10 


102 


2 


106 


15 


110 


29 


114 


15 


118 2 


121 


18 


124 


34 


127 


20 


20 


50 


3 


20 


99 


21 


103 


30 


107 


39 


111 


25 


115 11 


118 


31 


121 


50 


124 


39 


20 


40 


3 


30 


96 


35 


100 


44 


104 


53 


108 


38 


112 23 


115 


45 


119 


6 


122 





20 


30 


3 


40 


94 


12 


98 


11 


102 


10 


105 


54 


109 38 


113 


1 


116 


24 


119 


22 


22 


20 


3 


50 


92 


14 


95 


52 


99 


31 


103 


13 


106 55 


110 


18 


113 


40 


116 


43 


20 


10 


4 





89 


22 


93 


9 


96 


56 


100 


35 


104 14 


107 


38 


111 


2 


114 


7 


20 





4 


10 


87 


o 


90 


43 


94 


23 


97 


59 


101 35 


105 





108 


24 


111 


31 


19 


50 


4 


20 


84 


45 


88 


20 


91 


55 


95 


27 


99 


102 


24 


105 


48 


108 


57 


19 


40 


4 


30 


82 


32 


86 





89 


28 


92 


50 


96 11 


99 


42 


103 


12 


106 


22 


19 


30 


4 


40 


80 


21 


83 


13 


87 


5 


90 


30 


93 54 


97 


15 


100 


36 


103 


47 


19 


20 


4 


50 


78 


12 


81 


29 


84 


46 


88 


6 


91 25 


94 


44 


98 


2 


101 


14 


19 


10 


5 





76 


6 


79 


16 


82 


25 


85 


41 


88 57 


92 


15 


95 


32 


98 


44 


19 





5 


10 


74 


2 


77 


6 


80 


10 


83 


22 


86 33 


89 


47 


93 





96 


12 


18 


50 


5 


20 


72 





74 


57 


77 


53 


81 





84 7 


87 


19 


90 


30 


93 


41 


18 


40 


5 


30 


70 





72 


21 


74 


41 


78 


13 


81 45 


84 


53 


88 





91 


11 


18 


30 


5 


40 


68 





70 


46 


73 


30 


76 


27 


79 23 


82 


29 


85 


34 


88 


43 


18 


20 


5 


50 


66 


4 


68 


43 


71 


21 


74 


12 


77 3 


80 


6 


83 


8 


86 


15 


18 


10 


6 





64 


7 


66 


40 


69 


12 


72 


59 


74 45 


77 


43 


80 


40 


83 


46 


18 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle.- 



30(5 



LOGARITHM OF Tan 2 Z FOR LAT. 57° 30'. 





72° 


74° 


76° 


78° 


80° 


82° 


84° 


86° 




H. M. 


















H. M. 


6 


97435 


9-7182 


9-6929 


9-6727 


9-6526 


9-6384 


9-6242 


9-6171 


18 


6 10 


9-7654 


9-7383 


9-7111 


9-6887 


9-6663 


9-6496 


96328 


9-6231 


17 50 


6 20 


9-7866 


9-7576 


9-7286 


9-7041 


9-6796 


9-6606 


9-6416 


9-6289 


17 40 


6 30 


9-8072 


9-7765 


9-7458 


9-7192 


9-6926 


9-6709 


9-6492 


9-6337 


17 30 


6 40 


9-8275 


9-7951 


9-7627 


9-7341 


9-7056 


9-6818 


9-6580 


9-6398 


17 20 


6 50 


9-8471 


98131 


97790 


9-7486 


9-7181 


9-6917 


9-6652 


9-6444 


17 10 


7 


9-8663 


9-8307 


9-7951 


9-7627 


9-7304 


9-7021 


9-6738 


9-6504 


17 


7 10 


9-8847 


9-8476 


9-8104 


9-7763 


9-7422 


9-7117 


9-6812 


9-6555 


16 50 


7 20 


9-9029 


9-8642 


9-8256 


9-7897 


9-7538 


97213 


9-6888 


9-6606 


16 40 


7 3Q 


9-9206 


9-8805 


9-8404 


9-8029 


9-7653 


9-7308 


9-6964 


9-6657 


16 30 


7 40 


9-9377 


9-8962 


9-8547 


9-8155 


9-7763 


9-7395 


9-7028 


9-6703 


16 20 


7 50 


99540 


99112 


9-8684 


9-8276 


9-7868 


9-7484 


9-7100 


9-6748 


16 10 


8 


9-9702 


9-9260 


9-8818 


9-8395 


9-7972 


9-7574 


9-7176 


9-6801 


16 


8 10 


9-9854 


99399 


9-8945 


9-8508 


9-8070 


9-7652 


9-7234 


9-6841 


15 50 


8 20 


0-0013 


9-9537 


9-9070 


9-8619 


9-8167 


9-7733 


9-7298 


9-6883 


15 40 


8 30 


0-0144 


9-9666 


9-9187 


9-8722 


9-8258 


9-7806 


9-7354 


9-6924 


15 30 


8 40 


0-0284 


9-9794 


99304 


9-8826 


9-8349 


9-7882 


9-7416 


9-6971 


15 20 


8 50 


0-0415 


9-9914 


9-9413 


9-8923 


9-8433 


9-7954 


9-7464 


9-7006 


15 10 


9 


0-0544 


0-0032 


9-9520 


9-9019 


9-8518 


9-8025 


97532 


9-7048 


15 


9 10 


00659 


0-0139 


9-9619 


9-9104 


9-8590 


9-8085 


9-7580 


9-7079 


14 50 


9 20 


0-0771 


00239 


9-9707 


9-9184 


9-8661 


9-8144 


9-7626 


9-7111 


14 40 


9 30 


0-0877 


0-0337 


9-9796 


9-9263 


9-8730 


9-8200 


9-7670 


9-7140 


14 30 


9 40 


0-0979 


0-0430 


9-9880 


9-9338 


9-8795 


9-8256 


9-7716 


9-7172 


14 20 


9 50 


0-1072 


00514 


99956 


9-9405 


9-8854 


9-8304 


9-7754 


97196 


14 10 


10 


0-1166 


0-0598 


0-0030 


9-9473 


9-8916 


9-8355 


9-7794 


9-7227 


14 


10 10 


0-1242 


0-0671 


o-oioo 


99533 


9-8966 


9-8395 


9-7824 


9-7248 


13 50 


10 20 


0-1318 


0-0740 


0-0162 


9-9587 


9-9012 


9-8434 


9-7856 


9-7271 


13 40 


10 30 


0-1380 


0-0799 


0-0212 


9-9633 


9-9054 


9-8468 


9-7882 


9-7287 


13 30 


10 40 


0-1446 


0-0857 


0-0268 


9-9682 


9-9096 


9-8506 


9-7916 


9-7308 


13 20 


10 50 


01494 


0-0900 


0-0306 


9-9715 


9-9124 


9-8528 


9-7932 


9-7318 


13 10 


11 


01544 


0-0946 


0-0348 


9-9751 


9-9154 


9-8553 


9-7952 


9-7334 


13 


11 10 


0-1586 


0-0980 


0-0374 


9-9777 


9-9180 


9-8576 


9-7972 


9-7348 


12 50 


11 20 


01616 


o-ioio 


0-0404 


9-9804 


9-9204 


9-8596 


9-7988 


9-7359 


12 40 


11 30 


0-1644 


0-1034 


0-0424 


9-9822 


9-9220 


9-8608 


9-7994 


9-7365 


12 30 


11 40 


0-1666 


01055 


0-0444 


9-9838 


9-9232 


9-8620 


9-8008 


9-7375 


12 20 


11 50 


0-1674 


0-1062 


0-0450 


9-9844 


9-9238 


9-8623 


9-8008 


9-7375 


12 10 


12 


0-1678 


0-1067 


0-0456 


9-9849 


9-9242 


9-8627 


9-8012 


9-7377 


12 



Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 



PARALLACTIC ANGLE FOR LAT. 57° 30'. 



307 





72° 


74° 


76° 


78° 


80° 


82° 


84° 


86° 






H. M. 
































H. 


M. 


6 


64 c 


r 


66° 40' 


69 c 


12' 


72 c 


59' 


74 c 


45' 


77° 


43' 


80 c 


40' 


83 c 


46' 


18 





6 10 


62 


12 


64 24 


67 


5 


69 


47 


72 


28 


75 


22 


78 


16 


81 


19 


17 


50 


6 20 


60 


18 


62 39 


65 





67 


36 


70 


12 


73 


2 


75 


52 


78 


53 


17 


40 


6 30 


58 


26 


60 41 


62 


57 


65 


28 


67 


59 


70 


44 


73 


28 


76 


26 


17 


30 


6 40 


56 


33 


58 43 


60 


53 


63 


39 


65 


45 


68 


25 


71 


6 


74 


1 


17 


20 


6 50 


54 


43 


56 47 


58 


52 


61 


12 


63 


33 


66 


10 


68 


46 


71 


37 


17 


10 


7 


52 


53 


54 52 


56 


51 


59 


6 


61 


21 


63 


54 


66 


26 


69 


13 


17 





7 10 


51 


3 


52 57 


54 


51 


57 


2 


59 


12 


61 


39 


64 


6 


66 


50 


16 


50 


7 20 


49 


14 


51 3 


52 


52 


54 


58 


57 


3 


59 


25 


61 


48 


64 


28 


16 


40 


7 30 


47 


25 


49 9 


50 


53 


52 


54 


54 


54 


57 


11 


59 


28 


62 


4 


16 


30 


7 40 


45 


37 


47 17 


48 


56 


50 


51 


52 


46 


54 


58 


57 


10 


59 


42 


16 


20 


7 50 


43 


50 


45 25 


46 


59 


48 


49 


50 


39 


52 


47 


54 


54 


57 


21 


16 


10 


8 


42 


2 


43 32 


45 


2 


46 


47 


48 


32 


50 


36 


52 


40 


55 


1 


16 





8 10 


40 


16 


41 42 


43 


7 


44 


48 


46 


28 


48 


25 


50 


22 


52 


40 


15 


50 


8 20 


38 


29 


39 50 


41 


11 


42 


47 


44 


22 


46 


14 


48 


6 


50 


18 


15 


40 


8 30 


36 


43 


38 


39 


16 


40 


47 


42 


18 


44 


5 


45 


52 


48 





15 


30 


8 40 


34 


56 


36 9 


37 


21 


38 


47 


40 


13 


41 


56 


43 


38 


45 


39 


15 


20 


8 50 


33 


11 


34 19 


35 


27 


36 


49 


38 


10 


39 


47 


41 


24 


43 


20 


15 


10 


9 


31 


26 


32 31 


33 


35 


34 


52 


36 


9 


37 


40 


39 


12 


41 


4 


15 





9 10 


29 


40 


30 42 


31 


43 


32 


54 


34 


5 


35 


33 


37 





38 


45 


14 


50 


9 20 


27 


55 


28 51 


29 


48 


31 


4 


32 


21 


33 


34 


34 


48 


36 


27 


14 


40 


9 30 


26 


9 


27 2 


27 


54 


28 


58 


30 


1 


31 


17 


32 


34 


34 


7 


14 


30 


9 40 


24 


24 


25 13 


26 


2 


27 


1 


27 


59 


29 


12 


30 


24 


31 


51 


14 


20 


9 50 


22 


40 


23 25 


24 


10 


25 


4 


25 


59 


27 


4 


28 


10 


29 


33 


14 


10 


10 


20 


56 


21 35 


22 


14 


23 


6 


23 


58 


26 





26 





27 


16 


14 





10 10 


19 


8 


19 48 


20 


28 


21 


13 


21 


57 


22 


52 


23 


46 


24 


57 


13 


50 


10 20 


17 


22 


17 59 


18 


36 


19 


16 


19 


56 


20 


45 


21 


34 


22 


42 


13 


40 


10 30 


15 


36 


16 9 


16 


42 


17 


20 


17 


58 


18 


41 


19 


24 


20 


24 


13 


30 


10 40 


13 


56 


14 26 


14 


56 


15 


29 


16 


2 


16 


42 


17 


22 


18 


8 


13 


20 


10 50 


12 


8 


12 34 


13 





13 


28 


13 


56 


14 


32 


15 


8 


15 


49 


13 


10 


11 


10 


24 


10 47 


11 


10 


11 


31 


11 


52 


12 


23 


12 


54 


13 


32 


13 





11 10 


8 


50 


9 


9 


10 


9 


34 


9 


58 


10 


26 


10 


54 


11 


23 


12 


50 


11 20 


6 


50 


7 3 


7 


16 


7 


37 


7 


58 


8 


19 


8 


40 


9 


3 


12 


40 


11 30 


5 


22 


5 26 


5 


30 


5 


49 


6 


8 


6 


15 


6 


22 


6 


49 


12 


30 


11 40 


3 


42 


3 48 


3 


54 


3 


59 


4 


4 


4 


20 


4 


36 


4 


45 


12 


20 


11 50 


1 


51 


1 54 


1 


57 


2 





2 


2 


2 


15 


2 


28 


2 


36 


12 


10 


12 















































12 






Horizontal Argument, Declination. — Vertical Argument, Hour Angle. 
VOL. XXXIII. PART II. 



2 Y 



308 



LOG TAN 2 Z AND PAR. ANGLE (77) FOR LAT. 57° 30'. 







Decl. 88° 


Decl. 


88° 












Decl. 88° 


Decl. 


88° 






II. 


M. 


Log Tan 2 Z 


V 




11. 


M. 




H. 


M. 


Log Tan 2 Z 


V 




H. 


M. 








95403 


180° 


0' 


24 





6 





96100 


86° 


52' 


18 








10 


9-5403 


177 


52 


23 


50 




6 


10 


9-6134 


84 


22 


17 


50 





20 


9-5404 


174 


48 


23 


40 




6 


20 


9-6162 


81 


54 


17 


40 





30 


95404 


172 


8 


23 


30 




6 


30 


9-6182 


79 


24 


17 


30 





40 


95412 


169 


28 


23 


20 




6 


40 


9-6216 


76 


56 


17 


20 





50 


9-5416 


166 


52 


23 


10 




6 


50 


9-6236 


74 


28 


17 


10 


1 





9-5420 


164 


16 


23 







7 





9-6270 


72 





17 





1 


10 


9-5430 


161 


36 


22 


50 




7 


10 


9-6298 


69 


34 


16 


50 


1 


20 


9-5442 


158 


46 


22 


40 




7 


20 


9-6324 


67 


8 


16 


40 


1 


30 


-9-5458 


156 


10 


22 


30 




7 


30 


9-6350 


64 


40 


16 


30 


1 


40 


9-5472 


153 


34 


22 


20 




7 


40 


9-6378 


62 


14 


16 


20 


1 


50 


9-5486 


151 


2 


22 


10 




7 


50 


9-6396 


59 


48 


16 


10 


2 





9-5500 


148 


18 


22 







8 





9-6426 


57 


22 


16 





2 


10 


9-5512 


145 


42 


21 


50 




8 


10 


96448 


54 


58 


15 


50 


2 


20 


95536 


143 


4 


21 


40 




8 


20 


9-6468 


52 


30 


15 


40 


2 


30 


95550 


140 


28 


21 


30 




8 


30 


96494 


50 


8 


15 


30 


2 


40 


9-5572 


137 


50 


21 


20 




8 


40 


96526 


47 


40 


15 


20 


2 


50 


9-5596 


135 


14 


21 


10 




8 


50 


9-6544 


45 


16 


15 


10 


3 





95616 


132 


40 


21 







9 





9-6564 


42 


56 


15 





3 


10 


9-5632 


130 


6 


20 


50 




9 


10 


9-6578 


40 


30 


14 


50 


3 


20 


9-5662 


127 


28 


20 


40 




9 


20 


9-6596 


38 


6 


14 


40 


3 


30 


9-5678 


124 


54 


20 


30 




9 


30 


9-6610 


35 


40 


14 


30 


3 


40 


9-5706 


122 


20 


20 


20 




9 


40 


9-6628 


33 


18 


14 


20 


3 


50 


9-5730 


119 


46 


20 


10 




9 


50 


9-6644 


30 


56 


14 


10 


4 





9-5758 


117 


12 


20 







10 





9-6660 


28 


32 


14 





4 


10 


9-5780 


114 


38 


19 


50 




10 


10 


9-6672 


26 


8 


13 


50 


4 


20 


9-5808 


112 


6 


19 


40 




10 


20 


9-6686 


23 


46 


13 


40 


4 


30 


9-5836 


109 


32 


19 


30 




10 


30 


9-6692 


21 


24 


13 


30 


4 


40 


9-5866 


106 


58 


19 


20 




10 


40 


9-6700 


18 


54 


13 


20 


4 


50 


9-5896 


104 


26 


19 


10 




10 


50 


9-6708 


16 


30 


13 


10 


5 





9-5924 


101 


56 


19 







11 





9-6716 


14 


10 


13 





5 


10 


9-5952 


99 


24 


18 


50 




11 


10 


9-6724 


11 


52 


12 


50 


5 


20 


9-5980 


96 


52 


18 


40 




11 


20 


9-6730 


9 


26 


12 


40 


5 


30 


9-6010 


94 


22 


18 


30 




11 


30 


9-6736 


7 


16 


12 


30 


5 


40 


9-6044 


91 


52 


18 


20 




11 


40 


9-6742 


4 


54 


12 


20 


5 


50 


9-6072 


89 


22 


18 


10 




11 


50 


9-6742 


2 


44 


12 


10 


6 





9-6100 


86 


52 


18 







12 





9-6742 








12 






( 309 ) 



XIV.— On a Class of Alternating Functions. By Thomas Muir, LL.D. 

(Read 7th March 1887.) 



A glance at the expression 

(a — a)(a — 8) (a — y)(a ■ 



S) , (b-a)(b-8)(b-y)(b-S) 



(a — b)(a — c)(a — d) 



+ 



(e- a)(c-8)(c-y)(c-S) 
~*" (c-a)(c-b)(c-d) " 1 " 



(b-a)(b-c)(b-d) 

(d-aXd- 8)(d- y)(d-8) 
{d-a)(d-b)(d-c) 



is sufficient to verify the fact that it is symmetric with respect to a, b, c, d, and 
also with respect to a, fi, y, 8. It is likewise, although not quite so evidently, 
an alternating function with respect to the interchange 

(a b c d\ m 
a /3 y S } ; 

that is to say, if a and a be interchanged, and at the same time b and ft, c and 
y, d and S, the function is not altered in magnitude, but merely changes sign. 
With a little trouble, indeed, the expression can be transformed into 

(a + b + c + d) - (a + /3 + y + S), 

or say 2« — 2a 

This alternating function is only one of a large class to which it is proposed 
here to direct attention. It may be looked upon as in a certain sense the 
generator of the other members of the class, because they are derivable from it 
by prefixing to each of its component fractions a symmetric function of the three 
variables which occur only once in the corresponding denominator, e.g., the 
symmetric function bc + bd + cd prefixed as a factor to the first fraction, the like 
function ac + ad + cd prefixed to the second fraction, and so on. The various 
kinds of symmetric functions which may be used in this way as prefixed factors 
are best expressed in the form 



b m b n b r 




1 b b 2 


c m c n c r 


-^ 


1 c c 2 


d' n d n d r 




1 d d 2 



or 



\b m c n d r \ 



m, n, r, having any three values chosen from 0, 1, 2, 3, 4; for example, 
the above-mentioned instance 

bc + bd + cd 
is, in this form, 

I b°c 2 d 3 1 



, b chl 2 1 



VOL. XXXIII. PART II. 



2z 



310 DR THOMAS MUIR ON A 

The question then is — How can we by transformation set in evidence the 
fact that 

\b m c n d r \ (a-a)(a-{3)(a-y)(a-S) \ a m c»d r \ (b- a )(b- P)(b-y)(b-S) 
| b°c l d*\ ' ' (a-b)(a-c)(a-d) ' + | aVd 2 | * (b-a){b~c)(b-d) 

\aH n d r \ (c-g)(c-p)(c-y)(c-S) , \aH"c r \ (d-a)(d-8)(d-y)(d-S) 
+ \a°b l d?\' (c-a)(c-b)(c-d) ' + | a°b^ \ ' (d-a)(d-b)(d-c) 

is an alternating function with respect to the interchange 

/« b c d\ ? 
\a /3 y SJ- 

Since 

|&o c i rf2 | = £i(b,c,d) = (d-c)(d-b)(c-b), 
the fractions evidently have the same denominator, viz., 

(d — c)(d — b)(d — a)(c — b)(c — a)(b — a), 
or £K a bcd)\ 

so that, if we expand the original numerators in descending powers of a, of b, 
&c, the expression becomes 

^ a -J^ ) [-\ imc '' dr \U i -a^a + a^a/3-a'Sa^y + a/3yS} 
+ 1 a m fi»d r \{¥- b 3 Ha + & 2 2«/3 - bZafSy + a/3y 8 } 
- 1 a m ¥d r | { c 4 - c*2a + c 2 2a(3 - c2a/3y + a/3y8] 
+ \a">b»c>-\{d i -d^a + d^ap-d'Za(3y + a!3y8}~\ . 

This, when the coefficients of 2a, la/3, &a, are collected and condensed, 

= cj, b c ^ Mfl"^^! - | w»b"<rd s | Sa + I a m b n c r d? \ 2a/3 

- | a m b n c r d 1 2a/3y + I a m b n c r d° \ ?,a(3yS~\ , 

and no farther simplification is possible until the special values of m, n, r are 
given. 

Taking in order the ten different sets of special values 

0,1,2; 0,1,3; 0,1,4; 0,2,3; 

and denoting the whole expression by F m>nir> we see immediately that 



CLASS OF ALTERNATING FUNCTIONS. 311 

F °' 2 ' 4 = &(a, b, c, d) [ " ' a ° bW ' 2a ~ I a%2c4dl I ZaPy] , 
F °' 3 ' 4 = f *(g, 6, c, a 1 ) [ I a ° b3cid * I 2a _ I a ° 53c ^ 1 1 2 «£y] ' 

Fl ''' ,= gK»,Urf) [ ' al5W ' + ' aWd ° ' Sa8y< Q ' 

Fl ' 2 ' 4 = ftfg b c d) \_ ~ ! aWd? ' ' 2a + ' a ^ Vrf ° ! 2a/3y 5~1 , 

Fl ' 3 ' 4 = g*(g, &, e, d) [ I al&3c ^ 2 1 2a/3 + I ftl&3c4rf ° ' ^Wl - 
F 2 , 3 , 4 = ^ ^ c> rf) [ ~ I aWcW | 2a/3y + |aWd«|2aSy<f] . 



Now, from the theory of alternants it is known that 

\aWd 3 \ = ^(a,b, c,d), 
| a ojW | = £K a > h > c > d ) x 2a , 
| aObhW | - £*(a, &, c, d) x 2a& , 
| a°5W 4 1 = f Ha, b, c, d) x Zabc , 
| aWoP 1 = g*(a, b, c, d) x "Edbed ; 
and thus it follows that 

F , 1,2= 2a — 2a 

Fo, i, s = 2a& — 2a/3 , 

F ,i,4 = 2«&, 2a-2a/3.2a. 

F , 2, 3 = 2aZ>c — 2a/3y , 

F 0)2 ,4=2a&c . 2a — 2a/3y . 2a,- 

F a ,3,4=2a5c . 2a J 8-2a i 8y . 2a&, 

Fi, 2 ,3— 2a&ca'— 2a/3y<5 , 

Fi, 2, 4 = 2afcrt > . 2a — 2a/5yo* . 2a , 

F li3)4 = 2a&ca 7 . 2a/3-2a£y3 . 2a&, 

F 2 ,3,4 = 2a&ca' . 2a/3y — "EafiyS . 2,abc , 

all the expressions on the right being manifestly alternating functions with 
respect to the interchange 

/a b c d\ 

l« /? 7 Sj' 

These expressions are seen to be the ten determinants of the matrix 

1 2a 2a/3 2a£y 2a/3yo 
1 2a 2a& 2a&c ~Zabcd 

and consequently, if we represent this matrix by 

o" a - ! (T 2 <r 3 <r A 



312 DR THOMAS MUIR ON A CLASS OF ALTERNATING FUNCTIONS, 
the results take the form 

Fo,l,2 = | S 1 O- | , 
Fo, 1, 3 = i S 2 (T | , 



1^2,3,4 = I s 4 cr 3 I , 



where the suffixes on the right are got by subtracting from 4 each of those 
omitted on the left. 

With the help of this notation, also, we can combine all the results in one 
statement, viz. : — - 

Ifm, n, r co-ranged in order of magnitude be any three of the values 0, 1, 2, 
3, 4, and u, v arranged in order of magnitude be the remaining two, then 

\b m c"d r \ (a-a){a-fi)(a-y)(a-$) \ a m Pd r I _ (b-a)(b- /3)(b-y)(l— 8) 



Jb°cW\ (a-b)(a-c)(a-d) I a°c l d 2 I (6 - a)(b - c)(b - d) 

| a m b"d r | (c-a)(c-/3)(c-y)(c-S) \ a m b n c>- 1 (d-g)(d-jB){d-y)(d-8) 

+ \a b 1 d 2 \' ' (c-a)(c-b)(c-d) + | a°¥c 2 | ' (d-a){d-b){d-c) 

where s and a are explained by the examples s. 2 = lab, a 3 = 2<x/3y. 

The case where # = 4 has been given by Sylvester, being the subject of his 
unsolved problem No. 2810 in Mathematics from Educational Times, vol. xlv. 
p. 129. 

Of course the foregoing results are not at all confined to two sets of four 
variables [a, b, c, d), (a, /3, y, 8). Two sets of w variables have not been taken 
merely on account of inconvenience in writing. The typical term for the next 
case (two sets offve variables) is 

I b°c l d*e? | ' (a - b)(a - c)(a - d)(a - e) 
where (m, n, r, s) is a set of four values taken from 0, 1,2, 3, 4, 5. 



( 313 ) 



XV. — Expansion of Functions in terms of Linear, Cylindric, Spherical, and Allied 
Functions. By P. Alexander, M.A. Communicated by Dr T. Mum. 

(Read 20th December 1886.) 

The expansion of <f>(x) in terms of G Q (x), G^x), G 2 (x), &c, connected by a 
given law. being of great importance in mathematico-physical investigation, 
every method of effecting this expansion must have some interest for scientists. 

I therefore proceed to propose what I think to be a new method, in the 
hope that it may prove to be useful. 

Many special expansions of this nature have been effected by Fourier, 
Legendre, and others. 

After I had developed my method, my attention was called to two papers 
on this subject showing methods of development of great generality. The 
titles of the papers are — Konig, J., " Ueber die Darstellung von Functionen 
u. s. w.," Mathematische Annalen, v. pp. 310-340, 1871 ; and Sonine, N., 
"Recherches sur les fonctions cylindriques," &c, Mathematische Annalen, xvi. 
pp. 1-80, 1879. Konig, assuming that 

<p(x +x) = ¥ (x ) . G (x) + F^) . G,(x) + F 2 (x ) . G 2 (x) + &c. 

where G , G v G 2 , &c, are an infinite series of functions of x, connected by some 
given law, and also subject to the condition that when x is nearly equal to c, 
each of them is capable of expansion in ascending integral powers of (x — c), 
beginning in the case of G p (x) with (x— c) p , proceeds to show that the coefficients 
F (x ), F 1 (x ), &c, are to be deduced from the following — 

G (c).F (* ) =<j>(x +c), 
G (c) . F '(b ) = F (x ) . G '(c) + F^G^c) , 
G (c) . F "(* ) = F (* ) . G "(c) + F^ ) . Gt^e) + F 2 (* ) . G t "(«) , 
&c, &c. 

Sonine shows that 

8 (a+x) = A (a) . 8 (x)-2{A 1 (a)S 1 (x)- A 2 (a)S 2 (^) + &c.} 
if the series is convergent, where S (aj) and A (a) may be any functions what- 

VOL. XXXIII. PART IL 3 A 



314 MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 

ever of x and a consistent with convergency, and A («), A^a), A 2 («), &c, and 
S (x), S^x), S 2 (x), &c., are connected by the following relations :— 

A 1 («)=-J^[A («)],1 

d\ ' 

A w+1 + 2^-A ?l _ 1 = ) 



and 



i 

i 



1 dx I 



dS 



and hence 
and 
where . 



A n = (— i) n cosnAi- A , 
S w = ( — i) n cos n A . S , 

and \ and A are operations denned by 

a d 

% COS A, = -r , 

and 

d 
i cos A = 7 — • 
dx 

Konig's method seems to be much more general than Sonine's, as Konig's 
functions G , G l5 G 2 , &c, may be connected by any law, while Sonine's functions 
A , A x , A 2 , &c, are connected by one law only. But on the other hand, Konig's 
functions are limited by the condition that G p (x) must, when x nearly equals c, 
be capable of expansion in ascending integral powers of (x — c) beginning with 
(x— c) p , whereas Sonine's functions are subject to no such condition. 

Both methods give the expansion of (p(x) in terms of J (#), Ji(ai), J 2 ( x ), &c., 
Bessel's functions. But neither of them give the expansion 

<p(x) = A J n (k x) + Ai J„(/ci») + A 2 J n (k 2 x) + &c, 

where k , k^, k 2 , &c, are the roots of some equation of condition. 

The most general method of expansion I have seen is that of expansion in 
normal co-ordinates employed by Rayleigh throughout his Theory of Sound, 
which is so satisfactory that had I become acquainted with it somewhat earlier, 
I would probably not have sought after the following method : — 

The general problem is to determine A , A 1? A 2 , &c, so that when possible 
<p(x) = A G (x)+A 1 G 1 (x) + A 2 G 2 {x)+&c, . . . . (1) 
where G , G u G 2 , &c, are connected by some given law. 



MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 315 

The solution of this in all its generality has not yet been obtained, but in 
most of the particular cases which have been solved the method seems to be to 
operate on (1) with an operator 0„ such that 

O„.G m =0, (2) 

except m = n. 

And, therefore, 

O n . <j>(x) = A„O n . G n (x) 

A _ On.<p(x) .... (3) 

" On. Unix) 

Following this lead, I have found an operator of this nature in the case where 
G , Gi, G 2 , &c, are elementary solutions of the equation, 

(S+g)G = 0, (4) 

when g has the values g , g u g 2 , &c, derived from the condition 

*- G U = ° (5) 

where S and cr are operations which may have the forms 

d \ , v / d \2 



*= x »+ x .(^) +x 44y+ & (^ 



where X , X 1} X 2 , &c, and P , Pi, P 2 , &c, may be either constants or functions 
of x. 

The operator I have discovered for the solution of this problem is — 

o n= xs+</„n, =a (8) 

The proof is as follows : — 



But from (4), 






8 - G m = -9m- G m 




. * 2 -G m = -9j& m = 9j-& m 




* 3 -G m = <CSG m =-g m 3 G m 



(10) 



316 MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 

= (0n-9 m )' X <r& m + ° G <n 

+ *<*« ■ ■ (11) 



But from (5), 
Hence (11) gives — 



Hence from (3), 

Ab _ O»-0(s) 
0„.G„ 



i 
= if to is not = ™ ^ (12) 

0., I 



By the method of vanishing fractions, 



(m = n, x = a) 



\- Or. 



G m ) 









£<<r.GU)l 



Hence (13) becomes 



(13) 



A " = il <*■«»> L <14) 



which is the required solution. 

As new results, especially when very general, are liable to suspicion, I 
proceed to test this by a particular example whose solution can be otherwise 
found. 

Let 

H£f-m- t± ^ 2k ™ 

* In the proof of (11) it has been assumed that g m is less than g„. The same may be proved for 
f/ m greater than y„ by expanding {h + g n )~ l in the reverse order. 



ME P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 



317 



and 



■ = h+ 



dx 



(16) 



An elementary solution of (4) is in this case 



A.-1 

2 



or 



G n = (a V# K ) * J p+ ^ (« Jg n ) 



A.-1 



(17) ! 



where J and K are Bessel's functions of the first and second orders. 

Supposing then that it is possible to expand <p (x) in terms of the first of 
these and operating on (1) with the operator 



we have 



But 



O n = I dxX x G n 

(J>(x)x x G n dx = A /G G n x x dx + A l /G l G n x*dx+&c. 
o «-/ o «-/o 



G m G„x k dx 



f r dGn p dGm I 

^ X^dx-^dx ) x=a 



(18) 



(19) 



9m 9n 



AH h+ ^} _ 



gm—g n 



from (5) and (16) 



= -ak\ Gn<r - Gm \ from (16) 



= if m is not =n 

= — if m = n 





} 



from (5) 



(20) 



By the method of vanishing fractions, 

f a Glx^dx =-ah\ G ^.G m \ 

'* ^ 9 m -9n > (»»=».'<*=«) 



(21) 



\-l 



X-l 



Or 



G„ = (a; ^J 2 J ^.(aj ^„) + B„(a; >Jg n ) 2 K *_i(a? ^/^„) 



p+ 



P+- 



318 MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 

Again, 

n dx\_ dxj Y dx\__ dxj 
dx\ L dx ^ dx J) 

/<j>G n x k dx= - — I x^SG n dx, from (4) 
9n Jo 



or 



I — Qn —ix = a ffn <S 



a^G„8<£<i£ 

#11 



Similarly, 



/ 0.G n .a da: = / S<f>.G n x^dx 

Jo 3n 9 n J 

l) n v L - J x = a <S0 ) 

f a S<f>.G n .x'dx = ± { a^G^fy] -fh.(} n .x"dx } , 



and so on. 
Hence 



= « A {G n cr^ l + <5)- 1 0} ;r=(i .... (22) 



MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 319 

But 



A = 



ra 

j <p.G n .x x dx 



/V 



(23) 



00 ctoc 



Hence from (21) and (22) this becomes 



_ ft*[G„ . cr(8+g'»)- 1 0] a , =<i 



d 

v. dg n ) x=a 



(24) 



which verifies (14) for this case. 

If X = and p = (Fourier's Heat, ch. vii. and viii. ; Eayleigh's Sound, 
§ 135), then (23) or (24) will give an expansion of (f>(x) in linear functions 
(trigonometric), 

$(x)=A .^—cos(x l jg )+A 1 ^/—cos(xJff 1 )+&c. 

where g Q , g v &c, are the roots of 

a Jg . tan (a Jg) = ah . 

If X = l (Fourier's Heat, ch. vi.; Eayleigh's Sound, § 201), 

4>{x) = A . J p (x ,Jg Q ) + An . J p (x JgJ + &c, 

where g , g v &c, are the roots of 

JgJ' p (a Jg)+hJ p (a Jg) = , 
which gives an expansion of <f>(x) in cylindric or Bessel's functions. 

* Since writing this I have proved that if 8 = X 2 (-j-j + X X — + X 



A, --* 



f^dx 
" e 2 
4>.G n - — v dx 

A, 



Gn- — v dx 

but I find that Sturm and Liouville have anticipated me (Liouville's Journal de Mathematiques, vol.'., 
1836). 



320 MR P. ALEXANDER ON THE EXPANSION OF FUNCTIONS. 

If A = 2 (Fourier's Heat, ch. v.; Rayleigh's Sound, ch. xvii.), 

<j)(x) = A (x JgJ-Kfp+tfp M+A-ifa Jfh)~Wp+h( x M + &z-> 

where g , g v g 2 , &c. , are the roots of 

2a JgJ' p+i (a Jg) + (2ah-l)J p+h (a Jg) = , 

which gives an expansion of <f>(x) in terms of spherical functions (Kugel- 
functionen). 



( 321 ) 



XVI. — On Cases of Instability in Open Structures. By E. Sang, LL.D. 

(Read February 7, 1887.) 

In the course of some remarks on the scheme proposed for the Forth Bridge, 
which remarks are published in the eleventh volume of the Transactions of the 
Royal Scottish Society of Arts, I was led to enunciate, among other theorems, 
one of a somewhat unexpected character, to the effect that any symmetric 
structure built on a rectangular basis, having no redundant parts, and depend- 
ing on longitudinal strain alone, is necessarily unstable. This theorem was 
established by arguments restricted to the single matter under consideration ; 
it is one of an extensive class, and I now propose to discuss the subject from a 
general abstract point of view. 

The whole subject is evolved in the working out of two inverse geometrical 
problems and their corresponding mechanical applications. The relative posi- 
tions of a number of points being prescribed, we may have to secure these by 
linear connections ; or, the lengths of these connections being given, we may 
seek to discover the relative positions of the points. And we may have to 
compute the strengths needed to enable these connections to resist strains 
applied at the various points. 

The relative position of two points is determined by the length of the 
straight line joining them, and the material connection can only serve as the 
medium for the equipoise of equal and opposite strains applied at its two ends ; 
it can offer no resistance to stresses directed obliquely to it. The opposing 
pressures may be directed inwardly so as to cause compression, or outwardly 
so as to cause distension ; the former is an example of unstable, the latter an 
example of stable equilibrium. 

The instability in the case of compression is familiarly exemplified by an 
attempt to balance a load on the top of a walking-stick, or by the buckling of 
a long, thin rod ; stability can be obtained only by the use of something aside 
of the straight line. In the case of distension we have to observe that no 
member of a structure acts upon a contiguous member except by compression ; 
we do not pull an object toward us, we always push it ; each link of a chain 
pushes the other link ; the pulling is internal to the links themselves. Every 
case of stretching necessarily implies at each end compression changed first 
into transverse strain and then into distension. This phenomenon, which, from 
habit, we regard as simple, is indeed a most complex one, whose intimate 
nature as yet surpasses our understanding. Hence it is that, beyond the 

VOL. XXXIII. PART II. 3 B 



322 



EDWARD SANG ON CASES OF 



abstract arrangement of the parts as represented by straight lines, there is the 
problem, far more difficult, requiring much more constructive skill, of contriving 
the manner of the junctions. 

In general, the relative positions of three points, as A, B, C, are determined 
by the lengths of the three lines AB, BC, CA, joining them two and two. A 
pressure applied at the point A can be resisted by the linear members AB, AC 
only when its direction is in the same plane with them, and they must be 

enabled to offer resistance by pressures applied at 
B and at C, which again, if they be not in the 
direction BA, CA, must cause a stress on BC. 
Hence we have here a system of six pressures in 
equilibrium all having their directions in one plane. 
Let a A and />B be the directions of the pressures 
applied at A and at B, and let these be continued 
to meet in ; join also CO. According to the 
Fig. 1. known law of equilibrium, the strains on AB and 

on AC are proportional to the sines of the angles OAC and BAO, which again 

are represented by the doubles of the expressions and • where- 

fore, if we denote the strain on the member AB by the symbol AB, we have 

-ttt" • And on examining the equilibrium at B, 

we find also AB • -jjf- = CB • -™- , so that the direction of the pressure applied 

at C must also pass through the same point 0. 

Again, on comparing the pressure applied at A with the strain on AB, we 
find 

ABC AOC 




n ,. — BOA _ 

the equality AB • AB =CA 



aA : AB 



CA.AB CA.AU 



whence 



— AOC _ — ABC 
aA ' ~MT ~ Aii ' AB 



and it follows that the six expressions 

COB. BOA 



-j BOA .AOC 

aA ' AO 



bB 



BO 



6-C 



AOC .COB 
CO 



^ ABC. BO A g^ ABC. COB 



AB 



BC 



are all of equal value. 

On multiplying each of the first three by 

AO.BO.CO 
BOA.AOCCOB 



CA- 



ABC .AOC 
CA 



INSTABILITY IN OPEN STRUCTURES. 



323 



we get the equalities 



— BO. CO y~.-CO.AO 



COB 



AOC 



cC 



AO.BO 
BOA 




that is to say, the three external pressures applied at the points A, B, C 
balance each other just as if they had been applied directly to the point 0. 

When computing the internal strains caused by given external pressures, 
the area ABC occurs in every case as a division ; if, then, the three points 
were in one straight line, that is, if the area ABC were zero, the internal strains 
would become infinitely great, unless the applied pressures were all in the 
same line with them. Here we have the first and very well known example 
of instability in construction. 

If the point O be removed to a very great distance, the directions 
aA, b~B, cC of the external pressures become parallel as in fig. 2. The 
intermediate pressure, in this figure MB, must be op- 
posed to the direction of the others, its intensity being 
the sum of those at A and C. 

The relation of the strain on AC to the external 
pressure at B is then given by the formula 
__ — AX.CX 

ac-6b. AC-BX ; 

so that if B were shifted along the line BX nearer to X, Fig. 2. 

the strain on AC would be augmented in the inverse ratio of the new to the 

former BX ; but the pressures «A, bB, cC, would still remain proportional to the 

lines XC, CA, AX. Were B brought actually to X the strains would become 

infinite. 

It is much to be regretted that, in lesson books on mechanics, the beginner 
is taught the properties of this impossible straight lever, without a hint of 
caution in regard to it. The strains on the arms, even that upon the fulcrum, 
are left out of view. In this way hazy notions are engendered ; the load at A 
is said to balance that at C, although both be pressing in one direction. 

The relative positions of four points, as A, B, C, D, fig. 3, are in general 
fixed by the lengths of the six lines AB, CD, AC, BD, AD, 
BC joining them two and two ; these form the boundaries 
of a solid, called in Greek tetrahedron, which may get the 
English name fournib, shorter and quite as descriptive ; 
the potters call it crowfoot : it is the simplest of flat-faced 
solids. 

As in the triangle pressures applied at the corners can 
balance each other only when their directions meet in one Fig. 3. 

point ; so, reasoning by what is called analogy, we might infer that, of four 




324 



EDWARD SANG ON CASES OF 



pressures at the corners of a tetrahedron balancing each other, the directions 
must all tend to a single point. But this inference does not hold good ; it may 
be that no two of these directions meet at all. 

At each of the four points we have the equilibrium of four pressures, 
namely, the external pressure and the strains on the members meeting there. 
These strains can be computed when the direction and intensity of the applied 
pressure are known. 

Thus let us continue the direction dD of a pressure applied at D until it 
meet the plane of ABC in some point O, and let AO, BO, CO be drawn. We 
have then the equalities 

rfD JDA DB DC 
DO . ABC ~ DA . BOC ~ DB . CO A ~ DC . AOB ' 

The points A, B, C and O remaining as they are, if D were brought nearer 
to 0, the first of the above expressions would be augmented in inverse propor- 
tion to DO, and if D were brought actually to 0, this term would become 
infinite, the strains DA, DB, DC also infinite and the structure impossible. 

When, in such an arrangement as fig. 3, the resistances at A, B, C are in a 

direction parallel to dD, their intensities are proportional to the opposite 

triangles, so that 

dD_ ok 6B cC 
ABC _ BOC _ COA _ AOB ' 

and thus the distribution of the pressure among the ultimate resistances is 
independent of the distance DO. 

In fig. 3 the point is placed inside of the triangle ABC, and a pressure 
<i applied in the direction (TDO causes compression 
in all the three members, DA, DB, DC. In fig. 4 
is placed outside of the line AC, and, with 





B 




Pie. 4. 



Fig. 5. 



Tie. 6. 



pressure in the direction e/DO, the members DA, DC are compressed, while 
DB is distended. 

If here the point D were brought down to 0, the structure would take 
the form of a plane tetragon ABCD, with its two diagonals AC and BD, as 
shown in fig. 5. Such a structure can offer no resistance to pressures inclined 
to its plane. 

If the point D were on the straight line AC, as in fig. 6, it might seem that 



INSTABILITY IN OPEN STRUCTURES. 



325 



the five distances DA, AB, BC, CD, DB would suffice to secure the straight - 
ness of ABC ; but on consideration we perceive that the two triangles ABD, 
CBD are merely hinged upon the common line DB. 



In the cases of two, three, and four points, we have seen that the length 
of every line joining them in pairs is needed for fixing the relative positions; 
this rule does not hold for higher numbers. Thus, if a fifth point E be con- 
nected with three of the four corners of the tetrahedron ABCD, its relative 
position is determined, provided always that E be not in the plane of the three 
points with which it is joined ; so that nine lines suffice for five points. The 
line joining E with the fourth point of the tetrahedron would be redundant, 

In all such structures, three of the points, as A, B, C in fig. 7, must each 
have four concurring lines, and the remaining two, D and E, only three ; and 
if no four of the five points be in one straight line, the system is self-rigid. 

This rigidity will subsist although the two triple points D, E be in the 
same plane with any one pair of the quadruple ones, as in fig. 8, which is 
intended to show D, B, E, C as in one plane. The scheme then takes the 





Fig. 7. 



Fig. 8. 



Fig. 9. 



appearance of a pyramid, having A for its apex, and the quadrangle DBEC for 
its base. Thus the flatness of a tetragon may be secured by connecting each 
of its corners with a fifth point not in the same plane. 

Moreover, the system still remains rigid although the points D and E be 
both in one plane with AB also. In this case DBE, the meeting of two planes, 
must be a straight line, as shown in fig. 9. Thus we see that, for the establish- 
ment of three points in a straight line, two auxiliary points must be introduced, 
with seven additional linear members. 

We have now got a possible straight lever DBE. In order to examine the 
law of the balancing of pressures applied at B, D, E, we must trace out the 
strains on the various members, and their equilibriums at the five junctions, 
subject to the condition that there be no external pressure at A or at C. The 
result of this examination is, that the strains on the members are eliminated ; 
that the directions of the applied pressures must all pass through one point ; 



320 EDWARD SANG ON CASES OF 

and that their intensities must be proportional to the sines of the opposite 
angles, — this result being independent of the positions of the auxiliary points 
A and C. 

Does it thence follow that we may omit those points altogether ? Assuredly 
not ; for our whole investigation proceeded on the ground that each member 
transmits from its one end to its other end the strain with which it is 
accredited. 



Each additional point needs for its establishment three new linear members, 
so that in any self-rigid open structure, if n be the number of the points, there 
must be 3n — 6 linear connections; this formula failing only in the extreme 
case, M = 2. 



Hitherto we have been considering the self-rigidity of structures, and may 
now proceed to treat of the laws of stability in relation to the ground, taking 
first the case of a self-rigid structure to be kept firmly in position. 

In every case the support must be derived from points in the ground, which 
points necessarily form by themselves a rigid structure, so that our problem 
assumes the general form of " how to connect one rigid structure with 
another." If/ be the number of the points in the foundation, and n that of 
those in the supported structure, we have in all /+ n points in the compound, 
which must clearly be self-rigid. Hence the total number of linear members 
must essentially be 3f+3n — 6. But of these 3/— 6 are virtually included in 
the foundation, wherefore the number of the members above ground must in 
all possible cases be 3w. Of these, however, 3w — 6 are already included in the 
supported structure, and thus we arrive at the important general law, " that 
the number of linear supports must be neither more nor less than six when the 
supported structure is self-rigid." This most elementary of the laws of sup- 
port seems almost to be unknown, the enunciation of it takes even professional 
engineers by surprise. 

All our portable direction-markers, our theodolites, alt-azimuths, levelling 
telescopes, have to be supported above the ground at a height convenient for 
the eye. It is essential that the stationary part of each be firmly held ; yet in 
every case, with not one exception in the thousand, our geodetical instruments 
are set upon three slender legs, diverging almost from a point. In such an 
arrangement the steadiness in direction is derived exclusively from the stiffness 
of the legs, which, however, are very flexible. The well-known result is, that 
any strain in handling the instrument, even the pressure of a slight breeze, 
deranges the reading. 

More than fifty years ago an instrument maker in London, Robinson by 
inline, placed his beautifully made little alt-azimuths on a new kind of stand. 



INSTABILITY IN OPEN STRUCTURES. 



327 



He connected three points in the stationary part of the instrument with three 
points in the ground by means of six straight rods inclined to each other. In 
this arrangement, the stability in every direction is derived from the resistance 
to longitudinal compression, the flexure of the rods having an infinitesimally 
small influence. It takes essentially the form of 
the octahedron or sixnib, as in fig. 10 ; a self-rigid 
structure having six connected points. 

This beautiful Robinson stand keeps the alt- 
azimuth so firmly in position that, even during a 
heavy gale, the image of the moon may be seen to 
move without tremour across the cobwebs of the 
field-bar. Yet it has not been adopted by engineers 
and surveyors ; the exigencies of the photographer, 
however, have determined his recourse to it. 

It is not essential that the supports meet two 
and two as in this arrangement ; they may be quite 
detached, connecting six points in the supported Fig. 10. 

structure with six points in the ground ; but in all cases they must be so dis- 
posed that any dislocation whatever would imply a change in the length of 
some of them. 

It might have sufficed merely to remark that this condition excludes the 
parallelism of the supports ; but it is expedient to insist, seeing that, in the 
deplorable case of the Tay Bridge, the fabric was set upon two rows of upright 
columns. The opinion is still held that the effective base is equal to the whole 
breadth of such a structure, whereas the most casual examination may show 
that, no matter how broad the structure may be, its effective base is only that 
of a sinele column. 




When the superstructure is not rigid in itself, or indeed whether it be so or 
not, the entire number of the members above the ground must be thrice that 
of the supported points. If we attempt to do with fewer the fabric must fall ; 
if we place more we cause unnecessary internal strains. I hope in a subse- 
quent paper to treat of redundancy, meantime our attention may be confined 
to structures having the proper number of parts. 

If the supported points belong to one system they must be mutually con- 
nected, and, at the least, there must be as many of these connections as there 
are points, less one, wherefore the number of supports can never exceed twice 
the number of the points by more than one. 

Out of the endless variety of cases we may select one class for examination, 
that in which the supported points are connected so as to form a polygon, not 
necessarily all in one plane. The number of the connections being already n, 



328 



EDWARD SANG ON CASES OF 



that of the supporting members must be 2n, which may rest on 2n separate 
points in the ground, but which may be brought together in pairs or otherwise. 
If they be placed in pairs there are as many supporting as supported points. 

Robinson's octahedral stand shows this arrangement Avhen there are three 
supported points ; we shall now take the case when four points are supported 
from four points in the ground, as in fig. 11, where the connected points A, B, 
C, D are shown as supported by the eight members AE, EB, BF, FC, CG, GD, 
DH, HA. 

In general, that is when there is no regularity, such a structure contains all 
the elements of stability. The positions of the foundation points being known, 
if the lengths of the twelve members be prescribed, we shall have twelve equa- 
tions of condition whereby to compute the twelve co-ordinates of the four points 
A, B, C, D. Or, viewing the matter from the mechanical side, external pres- 
sures applied at A, B, C, D may be resolved into their elements in three 
assumed directions, x, y, z, and so may the stresses on the various parts ; there 

must be equilibrium at each of the points, 
in each of the three directions, and so 
again we have twelve equations whereby 
to compute twelve unknown quantities. 

The algebraist at once perceives that 
the resulting divisor (or determinant as 
it is called) may happen to be zero, in 
which case the stress becomes infinite ; 
that the dividend may be zero, showing 
that the particular member has no 
strain upon it ; or even that both the 
dividend and the divisor may be zero at 
once, showing the structure to be inde- 
terminate. But such investigations dis- 
tract the attention from the objects under 
consideration to their mere representative 
symbols, and do not carry intellectual 
conviction along with them. Their true 
and highly important office is to deter- 
mine accurately the various stresses, 
thereby enabling the constructor to ap- 
portion the strengths of the various parts. 
The determinateness, that is the 
stability, of a structure typified by fig. 11 
ceases when we introduce symmetry or even semi-regularity. Let, for example, 
the figures EFGH, ABCD be rhomboids, having their middle points and P 




Plan, 




Fig. 11. 



INSTABILITY IN OPEN STRUCTURES. 329 

in the same vertical line, in which case the opposite members are of equal 
lengths, AE to CG ; EB to GD, and so on. Such a structure is clearly 
instable. 

Since the lengths HA, AE are fixed, the point A must be on the circum- 
ference of a circle, having HE for its axis of rotation ; and similarly for the 
points B, C, D. If now we suppose the point A to be pushed inwards, the 
members AB, AD will push the points D and B outwards, and, consequently, 
C will move inwards by exactly as much as A ; the structure will adapt itself 
perfectly to its new position. In truth, we have here not twelve, we have only 
eleven data ; for, if one of the connections, say CD, were removed, and the 
structure thus made obviously mobile, the distance CD would yet remain 
always equal to AB ; that distance cannot be reckoned among the data. 

So much for the geometrical mobility ; let us examine the strains. Any 
horizontal pressure at A is decomposable into two, — one in the direction AB, 
the other in the direction AD. The stress AB transferred to the point B may 
again be decomposed into two ; the one of these in the plane EBF parallel to 
EF is completely resisted at E and F by the stresses EB, EF, but the other, 
perpendicular to EF, meets with no resisting obstacle ; it and the corresponding 
pressure at D may be counteracted by extraneous pressure there, or by a single 
pressure applied at C, equal to the pressure at A, and in the same direction 
with it. Thus the distortion of the fabric by an eastward pressure at A is 
prevented by a like pressure applied at C, not westward, but eastward also ; 
in respect, however, to the strains on EB, BF, HD, DG, the effects of these 
counteracting pressures are cumulative. 

These considerations would seem to warrant the conclusion that all struc- 
tures of this class are necessarily unstable ; however, before venturing to accept 
of this conclusion, it may be prudent for us to inquire whether the arguments 
on which it is founded be strong enough to bear such a weighty superstructure. 
Now the chief argument was that the longi- 
tudinal stress on AB, acting at B, tends to E Plan. 

turn the triangle EBF on EF as an axis ; but 
this tendency exists only so long as AB is out 
of the plane EBF, and ceases whenever AB 
comes to be in that plane ; in other words, when- 
ever AB is parallel to EF. Hence it follows 
that structures, represented in plan by fig. 12, Flg< 12 " 

having the two rhomboids ABCD and EFGH placed conformably, are rigid. 
The conclusion was not absolutely general. 

Though every rhomboid be not a rectangle, every rectangle is a rhomboid, 
and we might hastily thence conclude that these remarks concerning rhom- 
boidal structures may be at once extended to rectangular ones. But we have 

VOL. XXXIII. PART II. 3 C 




330 



EDWARD SANU ON CASES OF 



just come from seeing an example in which peculiarity precludes generalisation, 
and thus it is expedient for us to examine specifically the case of rectangular 
structures. 

The examination at once shows that the remarks made in regard to figs. 
11 and 12 apply when the rhomboids pass into the form of rectangles ; but the 
rectangle is symmetric, while the rhomboid is not so ; the arrangement of the 
diagonals, as shown in these figures, is unsymmetric, and it thus remains for us 
to inquire into the laws of symmetry. 



Plan. 




Fig. 13. 

eight diagonals, HA, AF 



If, as shown in fig. 13, the rectangle ABCD 
be placed vertically over and conformably with 
EFGH, the arrangement is symmetric ; it has 
already four out of the requisite twelve mem- 
bers, and the eight supports remain to be 
placed. 

These may be inserted symmetrically as the 
FC, CH ; DE, EB, BG, GD, but then the struc- 
ture becomes perfectly mobile ; the points A 
and C move towards or from the central axis, 
while B and D move from or towards it. 

In any other symmetric arrangement the 
four corner parts, EA, FB, GC, HD, must 
appear, leaving four members yet to be distri- 
buted. If one of these be placed as the 
diagonal AF, symmetry requires also DG, BE, 
and CH, as shown in fig. 14. 

The insecurity of this arrangement is ob- 
vious at a glance ; no more need to have been 
said about it, but for its adoption in the 
scheme for the central towers of the proposed 
Forth Bridge. It presents two instances of 
that most vicious arrangement, the flattened 
tetrahedron ; vicious because, while incapable 
of resisting any pressure not directed in its 
own plane, such a structure as EABF con- 
verts any twisting pressure into indefinitely 
exaggerated stress. It also presents two 
attempts to determine the shape of a quad- 
rangle by the lengths of the four sides. Were 
Fig. H. the three open figures, EFBA, ABCD, DCGH, 

replaced by flat rigid plates, we should have, turning on the four parallel hinges, 
EF, AB, DC, HG, a most familiar example of instability. 




Plarv 




INSTABILITY IN OPEN STRUCTURES. 



331 



Pl&TV. 




Fig. 15 



Among open structures built on a rectangular base, instability is not con- 
fined to those with rhomboidal tops ; for if, as in fig. 15, the triangle HAE be 
set up equal to GCF and EBF to HDC, so that 
AC may be parallel to EF and BD parallel to 
FG, the structure is movable. The diagonals AC 
and BD may be on one level and so cross each 
other, or the one may pass above the other at a 
distance on the plumb line OP. Since the 
three lines, AO, OP, PB, are mutually perpen- 
dicular — 

AB 2 =A0 2 +OP 2 +PB 2 
and CD 2 = CO 2 + OP 2 + PD 2 ; wherefore 

AB 2 + CD 2 = A0 2 + OC 2 +BP 2 +PD 2 +2.0P 2 . 

But the sum of BC 2 and AD 2 is equal exactly to the same quantity, and con- 
sequently 

AB2+CD 2 = BC 2 + DA 2 , 

so that one of these four is deducible from the remaining three ; there are then 
only eleven data in this structure, instead of the twelve needed for rigidity. 
But it is to be observed that a dislocation must change the horizontality of 
AC and BD, so that the mutability may be only instantaneous, as in the case 
of maximum or minimum. 



Passing now to the case of five supported points, we may remark that, by 
the introduction of a fifth point, a symmetric rigid 
structure may be built on a rectangular base. 

Thus, if we place, as in fig. 16, the rhombus 
ABCD vertically over the rectangle EFGH, and 
complete the construction as in fig. 11, there 
results a symmetric structure, which, like all those 
of the same class, is changeable. On assuming, 
however, a point Z in the vertical axis of the 
system, and connecting it with each of the points 
A, B, C, D, we get a fabric both symmetric and 
rigid. The rigidity is confirmed thus : — If, suppos- 
ing Z and its connections to be away, the points A 
and C be brought nearer, B and D would move 
apart ; now, in virtue of the connections AZ, ZC, 
the shortening of AB would cause Z to rise, while, in virtue of the connections, 
BZ, ZD, the widening of BD would bring Z down ; the opposition of these two 
tendencies keeps Z in its place. 




Fig. 16. 



332 



EDWARD SANG ON CASES OF 



Here, in order to support five points, sixteen members are conjoined, and 
yet there does not seem to be any redundancy ; moreover, the arrangement is 
quite symmetric. The equilibrium at each point gives rise to three equations 
of condition, and these fifteen equations cannot possibly serve to determine 
sixteen strains. But if we apply a pressure at any one of the five points, the 
fabric resists it, the various members are strained somehow, the law of equa- 
tions notwithstanding. The explanation of this paradox may afford an instruc- 
tive exercise to the student. 




Fig. 17. 



When the five points are arranged in the corners of a pentagon, each being 
carried by two supports, as shown in plan by fig. 17, the structure is rigid, pro- 
vided the polygons be convex. Of this we easily 
convince ourselves by supposing one of the con- 
nections, say EA, to be removed, and by ex- 
amining the motion of the link system thus left. 
The point A can move only in a circle, having 
KF for its axis ; let A be moved inwards, the 
member AB will then cause the triangle FBG 
to turn outwards on FG as a hinge ; BC will 
draw C inwards, CD will push D outwards, and 
lastly, DE will draw E inwards ; wherefore the 
distance AE will be shortened, and the member AE can be replaced only when 
the structure is brought back to its former position. 

Following this line of argument one step further, we see that in the case of 
a hexagon the first and last points would move, the one outwards, the other 
inwards, and that so the distance might remain unchanged. When the hexa- 
gons are semi-regular or halvable, the distance remains absolutely unchanged, 

and the structure is indifferent as to position. This 
same remark applies to all polygons of an even number 
of sides. 

If, however, the upper and lower polygons be placed 
conformably, as in fig. 18, the structure is rigid, whether 
the number of supported points be even or odd. 




Fig. 18. 



These truths may be illustrated experimentally by 
preparing a few isosceles triangles as AFB, having 
perforations at A and B, through which an elastic 
string may be passed. On connecting a number of these, say seven, by a con- 
tinuous thread, and spreading them out on a table, we form a flexible equal- 
sided heptagon, and when this is arranged regularly the points F are in the 



INSTABILITY IN OPEN STRUCTURES. 333 

corners of a larger regular heptagon. If we now trace on a flat board a regular 
seven-sided figure, intermediate in size between these two, and secure the 
points F of the triangles in holes made at the corners, we shall have erected a 
structure analogous to that shown in fig. 17, and shall find it to be rigid. 

If one of the triangles be removed, and the same process of construction 
followed with the remaining six, the resulting regular hexagonal structure is 
found to be instable. 

Another reduction of the number brings us to the pentagonal structure, 
which again is stable ; and still another removal gives the tetragonal instable 
fabric ; and, lastly, when only three triangles are left, we have Robinson's 
octahedral stand. 



The important distinction between the two cases of conformable or of un- 
conformable polygons may be illustrated by preparing two pairs of triangles, 
one pair as EAB, GCD, of fig. 12, the other pair as FBC, HDA, and by con- 
necting the sides, AB, BC, CD, DA, so as to form a flexible tetragon. 

When the feet, E, F, G, H, are secured in the corners of a rhomboid or of a 
rectangle, the structure is rigid, if AB, BC be parallel to EF, FG ; in all other 
cases it is instable. 



These cases of instability in open structures have been elicited by means of 
the simplest considerations in Geometry and Statics ; they lie indeed on the 
very surface of mechanical inquiry. They do not occur as isolated examples — 
they are arranged in extensive groups ; and, being found in those classes of 
structures which may be called shapely, they stand out as warning beacons to 
those engaged in engineering pursuits. 



VOL. XXXIII. PART II. 3 D 



( 335 ) 



XVII. — On the Fossil Flora of the Radstock Series of the Somerset and Bristol 
Coal Field (Upper Coal Measures). Part I. By Eobert Kidston, 
F.B.S.E., F.G.S. (Plates XVIII.-XXVIII.) 

(Bead April 4, 1887.) 

My attention for the last few years having been specially directed to the 
vertical distribution of the Carboniferous Fossil Flora, it is my intention to 
publish a series of papers dealing with this subject. 

While carrying on these investigations it has been necessary, in addition to 
visiting public and private collections, to visit several of the coal fields for the 
purpose of collecting specimens, as in almost no case have the smaller and less 
attractive species been secured, and, as a rule, only what strikes the ordinary 
collector as being "a fine specimen" is preserved, to the exclusion of many less 
striking but often more valuable examples. Hence our public collections, and, 
with few exceptions, also our private collections, give a very imperfect idea 
of the richness of the flora of the Carboniferous Formation of Britain. 

For the last four years I have annually paid a visit to the Radstock portion 
of the Somerset and Bristol Coal Field, with the object of collecting and 
examining the fossil flora of this area, from which were obtained several of the 
species described by Br.ongnia.rt, and which is probably richer in fossil plants 
than any other coal field in Britain, — not only in the number of species it con- 
tains, but also in their excellent state of preservation. 

A most important point in an investigation of this nature is to have the 
position of the beds from which the specimens have been derived accurately 
determined. In regard to the Radstock series of the Somerset and Bristol 
Coal Field, this qualification is amply fulfilled, making this area peculiarly suit- 
able as a starting point for investigations in the vertical distribution of the 
British Carboniferous flora. 

The geology of the Somerset and Bristol Coal Field, and especially the 
geology of the Radstock portion, has been fully worked out by several 
geologists, but it may not be out of place to introduce here a short geological 
sketch of this district, especially referring to the Radstock Series, from which 
all the specimens mentioned in the following list have been collected. 

The Somerset and Bristol Coal Field extends from Cromhall in Gloucester- 
shire to Frome in Somerset, and from Bath in the east to Nailsea and Clevedon 
on the west. 

VOL. XXXIII. PART II. 3 E 



336 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Its extreme length from north to south is 26 miles, and its width, from 
east to west (if the outlying Nailsea basin be included), is 24 miles. If the 
Nailsea basin be excluded, its width from Bath in the east to Bristol in the 
west is reduced to 12 miles. 

The Coal Measures are mostly covered by Secondary rocks, Jurassic and 
Triassic, which are unconformable to the underlying Palaeozoic strata. 

The Carboniferous Formation lies in a trough surrounded at intervals on 
the north, west, and south by the Old Eed Sandstone. 

The general geological structure of this coal field will be most easily under- 
stood by referring to Plate XVIII., which gives a reduced sketch of a section 
prepared by Mr J. M'Murtrie, F.G.S., for the Royal Coal Commission in 
1868. 

This section shows the Secondary Formations lying unconformably on the 
upturned edges of the Palaeozoic rocks. The centre of the basin is occupied 
by the Upper Division of the Coal Measures (Nos. in section 1, 2, 3). This 
rests on the Pennant Hock (No. 4), immediately beneath which is the Lower 
Division of the Coal Measures (5 and 6). Succeeding this is the Millstone 
Grit (7) and Carboniferous Limestone (8), which latter rests on the Old Eed 
Sandstone (9). 

It is necessary, however, to study in somewhat fuller detail the various 
horizons of the Coal Measures, — that is, all the Carboniferous rocks above the 
Millstone Grit. These, as already mentioned, resolve themselves into three 
great divisions, the Upper and Lower Divisions of the Upper Coal Measures, 
and the Pennant Rock. 

The Upper Division of the Coal Measures, attaining a thickness of about 
2200 feet, is separated into the Upper or Radstoek Series (1), and the Lower or 
Farrington Series (3), between which are interposed a characteristic series of 
Red Shales (2). 

The Upper Division (including the Radstoek and Farrington Series) is 
separated from the Lower Division by the Pennant Rock (4), which attains a 
probable thickness of from 2500 to 3000 feet. 

The Lower Division, of a thickness of about 2800 feet, is also divisible into 
two series, the upper of which is named the New Rock Series, and the lower the 
Vobster Series. 

These two series are not so clearly separable from each other as those of 
the Upper Division are by the intervention of the Red Shales, being separated 
rather on account of the character of the veins and the nature of the strata 
than by the occurrence between them of any unproductive characteristic 
stratum of rock. 

This coal field is traversed by many faults, some of which, especially the 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 33< 



Radstock great overlap fault, are well worthy of detailed study, but they do 
not fall in with the scope and object of these remarks. 

Having now taken a general survey of the ground, let us return again to 
the Upper Division of the Coal Measures, which embraces the Radstock and 
Farrington Series. 

The Radstock and Farrington Series occupy a basin, extending from Brisling- 
ton in the north to Kilmersdon in the south, and form an oval tract whose 
length from north to south is about 12 miles, and whose width from east to 
west is about 5 miles. 

There is another and smaller basin referable to the Radstock and Farring- 
ton Series, more particularly to the latter, which extends northwards from 
Pucklechurch for about 4 miles, with a width of about 2 miles. 

From this portion I have not collected, nor have I seen many specimens 
from it, but this is most probably due to deficient collecting, and not to 
the absence of specimens. 

I may mention here that the Radstock and Farrington Series, when viewed 
in their relation to the other coal fields of Great Britain, belong to their upper- 
most portion, and are the true Upper Coal Measures, altogether independently 
of their local position. 

The coal of the Upper or Radstock Series is chiefly worked in the neighbour- 
hood of Radstock, Writhlington, Midsomer-Norton, Camerton, Timsbury, and 
Paulton, and it is from the pits in the neighbourhood of these villages that 
most of the fossils referred to in this paper have been derived. 

The Radstock or Upper Series of the Upper Division contains eight veins, 

viz. : — 

The Withy Mills Seam, . . . . . . 1 ft. 4 in. 

Great Vein, . 
Top Little Vein, . 
Middle Vein, . 
Slyving Vein, 
Under Little Vein, 
Bull Vein, . 
Nine-inch Vein, 

Total, 

The total thickness of these veins is considerable, but in no case is the 
whole of it available at any one place. 

In the majority of cases I have found it impossible to note the vein from 
which the various fossils came, but the whole of the Radstock Series are so 
intimately connected that the knowledge of the actual veins from which the 
fossils originate appears to be of little importance in the present instance. 

The pits at which I have collected most are : — Braysdown Colliery, near 



2 „ 


2 


JJ 


1 „ 


4 


» 


2 „ 


2 


» 


2 


4 


99 


1 „ 


2 


JJ 


2 „ 


2 


» 


1 „ 






13 ft. 


8 


in. 



338 MR ROBERT KIDSTON ON THE FOSSIL FLORA. OF THE 

Kadstock ; this is one of the few collieries from which are worked the coals of 

both the Radstock and Farrington Series. Tyning and Ludlows Pits, Radstock, 

which are here treated as one, as they are connected and the debris of both is 

brought to the same rubbish tip near the Tyning Pit ; in the localities given 

for the species, Tyning and Ludlows Pits are recorded as " Radstock." Middle 

Pit and Wellsway Pit, Radstock ; Kilmersdon Pit and Lower Writhlington 

Pit, near Radstock ; the Camerton Pits ; and the Upper and Lower Conygre 

Pits, Timsbury. 

The veins belonging to the Radstock Series worked at these collieries 

are : — 

r Great Vein, Top Little Vein, Middle 



Braysdown Pit, . . < 


Vein, Slyving Vein, Under Little 


Vein, and Bull Vein. 


Ludlows and Tyning Pits, 


Do. 


Middle Pit, . 


Do. 


Wellsway Pit, 


Do. 


Kilmersdon Pit, 


Do. 


Lower Writhlington Pit, . 


Do. 


r Great Vein, Top Little Vein, Middle 


Camerton Pits, . . < 


Vein, Slyving Vein, and Under 


{ 


Little Vein. 


Upper Conygre Pit, 


Do. 


Lower Conygre Pit, 


Do. 



In addition to my own collecting, I have examined the specimens from the 
Radstock coal field in the Bath and Bristol Museums, and am indebted to 
the Rev. H. H. Winwood, F.G.S., for the use of specimens contained in the 
collection of the former, and to the Council of the Bristol Museum for a similar 
privilege ; and I am further under obligation to Mr E. Wilson, Curator of the 
Bristol Museum, for giving every facility for examining the specimens under his 
charge. 

I have also examined specimens from this coal field in the British Museum; 
University Museum, Oxford; Museum of the Geological Society of London; 
as well as some specimens from the same district in the Collection of the 
Geological Survey of England, in their Museum, Jermyn Street, London. 

I am, however, principally indebted to Mr J. M'Murtrie, F.G.S., Radstock, 
for kindly placing at my disposal, for the purpose of examination and descrip- 
tion, his fine collection of fossil plants from the Radstock Series. I am also 
further indebted to him for much information as to the geology of the neigh- 
bourhood, and from his various papers on the Geology of the Somerset and 
Bristol Coal Field the short geological sketch just given has been compiled.* 

* Those wishing fuller information on the geology of the Somerset and Bristol Coal Field will find 
it contained in the following papers and works : — Rev. Prof. W. Buckland and Rev. W. D. Cony- 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 339 

SYNOPSIS OF SPECIES. 

Fungi. 

Excipulites, Goppert, 1836, Diefossilen Farrnkrauter, p. 262. 

Excipulites callipteridis, Schimper, sp. 

Excipula callipteridis, Schimper, Traite d. paleont. veget., vol. i. p. 142, and Explanation to 

pi. xxxii. figs. 6, 7. 
Excipula callipteridis, "Weiss, Foss. Flora d.jiingst. Stk. u. d. Rothl., p. 19. 

Remarks. — On Sphenopteris neuropteroides. The minute fossils included 
here appear to be similar to those described by Schimper and Weiss as occur- 
ring on Callipteris conferta, Brongt. The central opening is not very well seen 
in our examples, which are situated on the limb of the pinnules between the 
veins. 

It is interesting to find that both Lesquereux (Coal Flora of Pennsyl., 
vol. i. p. 207, pi. xxxviii. fig. 2 ; P. anceps — Sphen. neiwopteroides) and Zeiller 
(Bull. soc. geol. de France, 3 e se>., vol. xii. p. 192) have noted the occurrence 
of these small fossils on the pinnules of Sphen. neuropteroides. 

There seems little reason to doubt that Excipulites comprises a group of 
minute parasitic fungi. 

Locality : — Radstock. 

beare, " Observations on the South-Western Coal District of England," Trans. Geol. Soc, ser. 2, vol. i. 
p. 210 ; G. C. Greenwell, " Notes on the Coal Field of East Somerset," Trans. N. of Eng. Inst, of 
Mining Eng., vol. ii. p. 258 ; G. C. Greenwell, " On the Southern Portion of the Somerset Coal 
Fields," Trans. S. Wales List, of Eng., vol. i. p. 147 ; H. Cossham, "On the Northern End of the 
Bristol Coal Field," Trans. N. of Eng. Inst, of Mining Eng., vol. x. p. 97 ; G. C. Greenwell, " On the 
Somersetshire Sections of the Bristol Coal Field," Trans. N. of Eng. Inst. Mining Eng., vol. x. p. 104 ; 
G. C. Greenwell and J. M'Murtrie, The Radstock Portion of the Somerset Coal Field, 1864, 8vo, 
Newcastle-on-Tyne ; R. Etheridge, " On the Physical Structure of the Northern Part of the Bristol Coal 
Basin," Proc. Cottsw. Nat. Field Club, vol. iv. p. 28 ; C. Moore, " On Abnormal Conditions of Second- 
ary Deposits where connected with the Somersetshire and South Wales Coal Basin, &c," Quart. Journ. 
Geol. Soc, vol. xxxiii. p. 449 ; J. M'Murtrie, " On the Carboniferous Strata of Somersetshire," Proc 
Bath Nat. Hist, and Antiq. Field Club, vol. i. No. 2, p. 45 ; J. M'Murtrie, " The Faults and 
Contortions of the Somersetshire Coal Field," ibid., vol. i. No. 3, p. 127; Report of the Commissioners 
appointed to inquire into the several matters relating to Coal in the United Kingdom, vol. i., 1871 ; 
John Anstie, The Coal Fields of Gloucestershire and Somersetshire and their Resources, 8vo, London, 
1873; J. M'Murtrie, "The Geographical Position of the Carboniferous Formation in Somersetshire, &c," 
Proc Bath Nat. Hist, and Antiq. Field Club, vol. ii. p. 454; J. M'Murtrie, "Notes on the Physical 
Geology of the Carboniferous Strata of Somersetshire and associated Formations," Somerset Arch, 
and Nat. Hist. Soc, 1875 ; J. M'Murtrie, "The Somersetshire Coal Fields, and the Method of work- 
ing thin Seams in the Radstock District," Proc S. Wales Inst, of Eng., vol. xii. No. 5, p. 424 ; 
H. B. Woodward, Memoirs of the Geological Survey, Geology of East Somerset and the Bristol Coal 
Fields, 1876. 



340 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

EQUISETACE.E. 

Calamites, Suckow, 1784, Act. Acad. Tkeocl. Palat, vol. v. p. 359. 

Group I. Calamitina (emend.). Weiss, 1884, Steinkoiden-Calamarien, 

part ii. p. 59. # 

Calamitina (Calamites) varians, var. insignis, Weiss. 

Cal. (Calamites) varians, var. insignis, Weiss, Steinkoiden-Calamarien, part ii. p. 63, pi. i.; pi. xxviii. 

fig. 1. 
Calamites varians, Germar, Vers. v. Wettin u. Ldbejun, p. 49, pi. xx. figs. 1-3. 

Remarks. — Rare. 
Locality : — Camerton. 

Group II. — E ucalamites, Weiss, 1884, Steinkoiden-Calamarien, 

part ii. p. 96. 

Eucalamites (Calamites) (cruciatus) senarius, Weiss. 

Calamites (cruciatus) senarius, Weiss, Steinkoiden-Calamarien, part ii. p. 114, pi. xiii. fig. 2. 
Calamites approximatus, L. & H., Fossil Flora, vol. iii. pi. ccxvi. 

Remarks. — The University Museum of Oxford possesses a fine specimen of 
this species from Camerton, which is the original of pi. ccxvi. of Lindley and 
Hutton's Fossil Flora, In the description of their plate (which is a reduced 
figure of the fossil), the authors say — " It agrees in a striking manner with 
the figures of Aims and Adolphe Bkongniart, with the addition of a 
number of pits placed on the articulations, in a quincuncial manner, as in 
Calamites cruciatus. Hence it is probable that the latter proposed species will 
require to be reduced to C. approximatus." 

The specimen referred to in the above quotation, and figured by the authors 
of the Fossil Flora on their plate ccxvi., belongs, however, to an entirely 
different group of Calamites from that in which C. approximatus is now placed. 

In Eucalamites, which includes the Camerton plant, every node bears 
branches. Fn Calamitina, on the other hand, in which C approximatus, Brongt., 
is enrolled, the branch-bearing nodes are separated by a greater or less number 
of nodes that do not produce branches. 

The Camerton specimen of Calamites (Eucalamites) senarius, which is a 
compressed stem removed from the matrix, measures about 15 inches in length 
and about 3f inches in width at its lower extremity. It consists of sixteen 
perfect internodes and portions of two incomplete ones — one at each end of 
the fossil. On the circumference of each node are borne six branch scars. 
The internodes decrease slightly in length from below up, but in a somewhat 
irregular manner. Their exact measurement is — 

* Abhandl. z. geol. specialdcarte v. Freusseu a. Thurinyischen Staateu, Band v. part ii. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 341 




"7 cm. incomplete. 



1-6 



1st Internode, 
2nd „ 

3rd „ 
4th „ 

5th „ 

6th „ 
7th 

8th „ 

9th „ 

10th „ 

11th „ 
12th „ 

13th „ 

14th ;, 

15th 
16th „ 

17th „ 
18th „ 

36-7 cm. 

Fig 1. Eucalamites cruciatus senarius, Weiss ; Camerton (f nat. size). 

Locality : — Camerton. 

Eucalamites (Calamites) ramosus, Artis. 

Calamites ramosus, Artis, Antedil. Phyt., pi. ii. 

Calamites ramosus, Brongt., Hist. d. veget. foss., p. 127, pi. xvii. figs. 5 6. 
Calamites ramosus, Zeiller, Veget. foss. du terr. liouil., p. 15. 
J2al. {Eucalamites) ramosus, Weiss, Steinltohlen-Calamarien, part ii. p. 98, pis. ii. fig. 3 ; v. figs. 
1-2 ; vi. ; vii. figs. 1-2 ; viii. figs. 1, 2, 4 ; ix. figs. 1,2; x. fig. 1 ; xx. figs. 1, 2. 
Calamites nodosus, L. & H., Foss. Flora, vol. i. pis. xv., xvi. 
Calamites nodosus, Lebour, Illustrations of Foss. Plants, p. 3, pi. ii. ; p. 7, pi. iii. 
Calamites carinatus, Sternb., Vers., i. fasc. 3, pp. 36 and 39, pi. xxxii. fig. 1 ; fasc. iv. p. xxvii. 

As foliage : — 

Annularia radiata, Brongt., Prodrome, p. 156. 

Annularia radiata, Zeiller, Veget. foss. du terr. liouil., p. 24, pi. clx. fig. 1. 
Asteropliyllites radiatus, Brongt., Class d. veget. foss., p. 35, pi. ii. fig. 7. 
Aster opliyllites foliosus, L. & H., Foss. Flora, vol. i. pi. xxv. fig. 1. 



2- 


J3 




2-2 


» 




1-8 


■9> 




21 


3> 




2-3 


» 




1-8 


)) 




1-9 


» 




2-5 


»» 




2- 


» 




2-4 


7) 




2-5 


» 




2-7 


J) 




2-7 


w 




2-7 


99 




27 
•1 




ncomplete 



342 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Asterophyllites foliosus, Geinitz, Vers. d. Steinkf. in Sachsen, p. 10, pi. xvi. figs. 1-3 (fig. 4 ?) (excl. 
pL xv.). 

Remarks. — Rare. 

Locality : — Rad stock. 

Group III. — S tylocalamites, Weiss, 1884, Steinkohlen-Calamarien, 

part ii. p. 119. 

Stylocalamites (Calamites) Suckowii, Brongt. 

Calamites Suckowii, Brongt., Hist. d. veget. foss., p. 124, pi. xiv. fig. 6 ; pi. xv. figs. 1-6 ; pi. xvi. 

figs. 2, 3, 4 (1 ?). 
Calamites Suckowii, Feistmantel, Vers. d. hohm. Kohlenab., p. 102, pi. ii. figs. 3, 4; pi. iii. figs. 1, 2 ; 

pi. iv. figs. 1, 2, pi. v.; pi. vi. fig. 1 (excl. as fruit H. carinata). 
Calamites Suckowii, Geinitz, Vers. d. Steinkf. in Sachsen, p. 6, pi. xiii. figs. 1-6. 
Calamites Suckowii, Roehl, Foss. Flora d. Steink. Form. Westph., p. 9, pi. i. fig. 6 ; pi. ii. fig. 2. 
Calamites Suckowii, Weiss, Steinkohlen-Calamarien, part i. p. 123, pi. xix. fig. 1 (1876); part ii. 

- p. 129, pi. ii. fig. 1 ; pi. iii. figs. 2, 3 • pi. iv. fig. 1; pi. xxvii. fig. 3 (1884). 
Calamites Suckowii, Kidston, Catal. Palceoz. Plants, p. 24. 
Calamites decoratus, Artis, Antidel. Phyt., pi. xxv. 
Calamites decoratus, Brongt. (in part), Hist. d. veget. foss., p. 123, pi. xiv. figs. 1, 2 (excl. figs. 3, 4). 

Remarks. — Not common. 

I have observed two specimens of this species from Camerton, — one in the 
Bristol Museum, the other kindly given me by Mr G. West, — which show the 
peculiarity of a double row of tubercles, one row at each extremity of the ribs ; 
thus each nodal line has a row of large tubercles immediately below it, and a 
row of smaller tubercles immediately above it. The same peculiarity is figured 
by Brongniart (C. decoratus, Brongniart (not Artis), Hist. d. veget. foss., pi. 
xiv. figs. 3, 4) and Weiss (C. ramosus, Steinkohlen-Calamarien, part ii. p. 108, 
pi. ix. fig. 2). It is shown from the specimen given me by Mr West, which is a 
portion of the stem near its base, that the larger tubercles occupy the normal 
position, viz., the upper extremities of the ribs, and the smaller tubercles the 
lower extremity. Weiss's figure is therefore, as suspected by him, drawn in 
inverted position. My Camerton specimen also shows the further peculiarity, 
likewise mentioned by Weiss in the description of his example, that many of 
the ribs, instead of alternating at the nodes in a normal manner, are exactly 
opposite. This latter abnormality, however, in the case of a few ribs, is not a 
very uncommon phenomenon on stems of Calamites. 

Localities : — Radstock ; Camerton. 

Stylocalamites (Calamites) cannseformis, Schloth. 

Calamites canna-formis, Scblotbeim, Pet refactenkunde, p. 398, pi. xx. fig. 1. 

Calamites cannoeformis, Brongt., Hist. <l. vSgit. 'foss., p. 131, pi. xxi. 

Cab i mil's '■anna-formis, Lindley and Hutton, Foss. Flora, vol. i. pi. lxxix. 

Calamites canncuformis, Weiss, Foss. Flora d.junget. Stk. ti. d. Moth?., p. 115. 

Calamites canncnformis, Zeiller, Vi'gi't. foss. du ten: houi?., p. 16. 

Calamites pachydermia, Brongt., Hist. d. veget. foss., p. 132, pi. xxii. 

Remarks. — A few stems have been met with that should perhaps be 
referred to this species, which, however, appears to me to be a very ill-defined 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 343 

one, and in which are often placed large and badly -preserved stems that pro- 
bably belong to C. Suckoivii or some other species. 

The type figure of C. cannceformis represents the terminal portion of a 
stem which does not seem to have been well preserved, hence there is diffi- 
culty in recognising the plant really meant by Schlotheim. 

Localities : — Camerton ; Welton Hill, Midsomer-Norton. 

Stylocalamites (Oalamites) Cistii, Brongt. 

Catamites Cistii, Brongt., Hist. d. veget. foss., p. 129, pi. xx. 

Catamites Cistii, Geinitz, Vers. d. Steinkf. in Sachsen, p. 7, pi. xi. figs. 7, 8 ; pi. xii. figs. 4, 5 ; 

pi. xiii. fig. 7. 
Catamites Cistii, Schimper, Traite de paleont. veget., vol. i. p. 313. 

Remarks. — More frequent than the foregoing species ; not common, how- 
ever. 

Localities : — Kadstock ; Braysdown ; Camerton ; Wellsway ; Lower Writh- 
lington. 



'&' 



Calamocladus, Schimper, 1869, Traite d. paleont. veget, vol. i. p. 323. 
Calamocladus equisetiformis, Schloth., sp. 

Calamocladus equisetiformis, Schimper, Traite d. paleont. veget., vol. i. p. 324, pi. xxii. figs. 1-3. 
Asterophyllites equisetiformis, Germar, Vers. v. Wettin u. Lobejun, p. 21, pi. viii. 
Asterophyllites equisetiformis, Zeiller, Veget. foss. du terr. Jwuil., p. 19, pi. clix. fig. 3. 
Hippurites longifolia, L. & H., Fossil Flora, vol. iii. pis. cxc, cxci. 

Casuarinites equisetiformis, Schlotheim, Flora d. Vorwelt, p. 30, pi. i. figs. 1, 2; pi. ii. fig. 3. 
Annularia ealamitoides, Schimper, Traite d. paleont. veget., vol. i. p. 349, pi. xxvi. fig. 1. 

Remarks. — Not very frequent. 

Localities : — Radstock ; Braysdown ; Wellsway ; Upper Conygre Pit ; 
Kilmersdon. 

Annularia, Sternberg, 1820, Vers, einer Geog. Botan. Darstellung d. Flora d, 

Vorwelt, fasc. 2, p. 32. 

Annularia stellata, Schloth., sp. 

AnnulariasTellata, Zeiller, Veget. foss. du terr. houil., p. 26, pi. clx. figs. 2, 3. 
Casuarinites stellatus, Schloth., Flora d. Vorivelt, p. 32, pi. i. fig. 4. 
Annidaria longifolia, Brongt., Prodrome, p. 156. 

Annularia longifolia, Germar, Vers. d. Wettin u. Lobejun, p. 25, pi. ix. 
Annidaria longifolia, Weiss, Foss. Flora d. jilngst. Stk. u. Rothl., p. 30. 
Asterophyllites longifolia, L. & H., Foss. Flora, vol. ii. pi. cxxiv. 
Asterophyllites longifolia, Binney, Pcdceontological Soc, 1868, p. 28, pi. vi. fig. 3. 

As its fruit : — 

Stachannularia tuberculata, "Weiss, Steinkohlen-Calamarien, vol. i. p. 17, pi. i. figs. 2-4; pi. ii. 

figs. 1-3, 5 (left); pi. iii. figs. 3-10, 12. 
Stachannularia tuberculata, Kidston, Catal. Palceoz. Plants, p. 56. 
Buckmannia tuberculata, Sternberg, Vers., i. fasc. 4, p. xxix. pi. xlv. fig. 2. 

VOL. XXXIII. PART II. 3 F 



344 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Remarks. — Frequent. Sterzel* notes the occurrence of specimens of Annu- 
laria steUata with Stachannularia tuberculata organically united, which proves 
what had previously been suspected, that this cone is the fruit of Annularia 
stellata. 

The cones of this species are rare in the Radstock Coal Field. 

Localities: — Radstock.; Braysdown ; Camerton ; Upper Conygre; Lower 
Conygre ; Paulton ; Kilmersdon. 

Annularia sphenophylloid.es, Zenker, sp. 

Annularia sphenophylloides, Geinitz, Vers. d. Steinkf. in Saclisen, p. 11, pi. xviii. fig. 10. 
Annularia sphenophylloides, Schimper, Traite d. paleont. veget., vol. i. p. 347, pi. xvii. figs. 12, 13. 
Annularia sphenophylloides, Sterzel, Zeitsch. d. deut. geol. Gesell., voL xxxiv. p. 685, pi. xxviii. 
Annularia sphenophylloides, Weiss, Foss. Flora d. jiingst. Stk. u. Rothl., p. 131. 
Annularia sphenophylloides, Zeiller, Veget. foss. du terr. houil., p. 25, pi. clx. fig. 4. 
Annularia spthenojihylloides, Kidston, Catal. Palmoz. Plants, p. 44. 
Galium splienophylloides, Zenker, Neues Jahrb., 1833, p. 398, pi. v. fig. 6. 
Annularia hrevifolia, Brongt., Prodrome, p. 156. 

As its fruit : — 

Stachannularia calathifera, Weiss, Steinkohlen-Calamarien, vol. i. p. 27, pi. iii. fig. 11. 

Remarks. — Frequent. Some large slabs were entirely covered with the 
leaves of this plant. STERZELt has shown that the little cones, described by Weiss 
as Stachannularia calathifera, are the fruit of this species. The fruit is rare in 
the Radstock Coal Field, having only been found once at Radstock. 

Localities : — Radstock ; Upper Conygre ; Lower Conygre ; Camerton ; 
Braysdown ; Kilmersdon. 

(?) Rhizocarpete. 

Sphenophyllum, Brongniart, 1822, Sur la Classification d. veget. foss., p. 34. 

Sphenophyllum emarginatum, Brongniart. 

Sphenophyllum emarginatum, Coemans and Kickx, Bull. Alcad. roy. Belgique, 2° ser. vol. xviii. 

p. 144, pi. i. fig. 2 ; pi. ii. figs. 1-3. 
Sphenophyllum emarginatum, Geinitz (in part), Vers. d. Steinkf. in Saclisen, p. 12, pi. xx. figs. 1, 

3,4. 
Spheno])hyllum emarginatum, Schimper, Traite d. paleont. veget., vol. i. p. 339, pi. xxv. figs. 15, 16. 
Sphenophyllum Schlotheimii, L. & H. (not Brongt.), Fossil Flora, vol. i. pi. xxvii. 

Remarks. — Frequent. 

Localities : — Radstock ; Braysdown ; Camerton ; Paulton ; Upper Conygre ; 
Lower Conygre. 

Fructification. 

Macrostachya, Schimper, 18G9, Traite d. paleont. veget., vol. i. p. 332. 

Macrostachya infundibuliformis, Brongniart, sp. 

Macrostachya- infundihuliformis, Schimper, Traite d. paleont. veget, vol. i. p. 133, pL xxiii. 
iigs. 15-17 (cxcl. figs. 13, 14). 

* Zeitsch. d. deut. geol. Gesell, 1882, p. 685. f Loc. cit., p. 685. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 345 

Macrostachya infundibuliformis, "Weiss, Steinkohlen-Calamarien, part i. p. 71, pi. vi, figs. 1-4;: 

pi. xviii. figs. 1, 3, 4 (1876) ; part ii. p. 197 (1884). 
Equisetum infundibuliforme, Brongt. (in part), Hist. d. veget. foss., p. 119, pi. xii. figs. 14, 15 

(excl. syn. and fig. 16). 
Huttonia carinata, Germar, Vers. v. Wettin u. Lbbejun, p. 90, pi. xxxii. figs. 1, 2. 
Macrostachya carinata, Zeiller, Veget. foss. du terr. houil., p. 23, pi. clix. fig. 4. 
Equisetum, Brongt., Class, d. veget. foss., p. 90, pi. iv. fig. 4. 

Remarks. — Very rare ; only two examples having been found. 
Localities : — Radstock ; Kilmersdon. 

Filicace^:. 

Sphenopteris, Brongniart, 1822, Sur la Classification d. veget. foss., p. 33. 

Sphenopteris tenuifolia, (Brongt. ?) Gutbier. 
Plate XIX. fig. 2. 

(?) Sphenopteris tenuifolia, Brongt., Hist. d. veget. foss., p. 190, pi. xlviii. fig. 1. 

Sphenopteris tenuifolia, Gutbier, AbdriicJce u. Vers. d. Zwiclmuer Schwarzlwhl, p. 39, pi. v. fig. 10; 

pi. x. fig. 9. 
(?) Clieilanthites tenuifolius, Gb'ppert, Syst. fil. foss., p. 241. 

Description. — Frond tripinnate ; primary (?) and secondary pinnae alternate, 
lanceolate ; pinnules alternate, lanceolate ; lower pinnules divided into numerous 
(as many as fourteen) segments ; the lower segments are again divided into 
four to six simple or bifid lanceolate acute teeth ; upper pinnules less divided, 
bearing simple, bifid or trifid acute lanceolate segments, into each of which 
extends a vein. Rachis of pinnae thin. Fruit borne at the extremities of the 
secondary (?) pinnae, and situated at the margin of the pinnule segments. 

Remarks. — The specimen, of which a drawing is given natural size, shows 
two (?) primary pinnae lying parallel to each other. As their parent rachis is 
not shown, their entire length cannot be estimated. The portions of the pinnae 
preserved measure about 6 inches each. 

This, the only example which I have seen, is beautifully preserved, and 
shows the most minute details of the pinnule cutting. The lower pinnules of 
the lower secondary pinnae are much divided into broadly lanceolate segments, 
and the lower segments are again divided into a few simple and bifid acute 
lanceolate teeth, into each of which runs a vein. A careful drawing of one of 
these pinnules, magnified three times, is given on Plate XIX. fig. 21). An upper 
pinnule, also enlarged three times, is shown at fig. 2a ; the segments of this are, 
with one exception, bifid, but these details vary according to the position of 
the pinnule on the pinna, the uppermost pinnules being even less divided. 

The fruit is borne on the upper secondary pinnae, apparently at the margins 
of the pinnules. Its structure is not well shown, the fruit appearing as little 
indistinct groups at the extremities of the ultimate segmentation. Owing to the 
somewhat indistinct details of the fruit, I am led to believe it had not reached 
maturity, as the other parts of the specimen show their structure exquisitely. 



346 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

I may note here that many of the Pecopteroids from this Coal Field are 
found in fruit, but always in an immature condition, and seldom show their 
structural details clearly, though in all other points the preservation of the 
fossils is very fine. 

The mode of fructification of Sphen. tenuifolia appears to be similar to that 
of Sphen. Giitzoldi, as figured by Gutbier.* 

Stur regards as distinct species the Sphen. tenuifolia, Brongt., and the 
plant figured under that name by Gutbier, and has described a third species, 
Sphenopteris [Calymmotlieca) subtenuifoliaA 

Brongniart states in his description of his Sphen. tenuifolia that the speci- 
men was preserved in a coarse-grained sandstone ; hence he was not satisfied 
as to the thorough accuracy of his enlarged drawing of the pinnule. If, how- 
ever, we compare the pinnule, as represented by Brongniart, with that on 
our PI. -XIX. fig. 2a, their similarity is very striking. On the other hand, 
Brongniart's plant has apparently a more rigid growth, and the main rachis 
is very thick for the size of the pinnae ; on our example the main rachis is 
unfortunately not shown. 

With the fern from Zwickau, figured by Gutbier as Sphen. tenuifolia, our 
example agrees perfectly, his fig. 9, pi. x. being apparently identical with my 
fig. 2. The enlargement of the other example given by Gutbier in his pi. v. 
fig. 10a, does not seem to differ essentially from my fig. 2a, though the segments 
of the pinnules of his figure are shown to be a little stouter than in the 
Somerset plant. 

Stur's Sphen. (Calymmotheca) subtenuifolia is very closely allied to Sphen. 
tenuifolia, if really distinct from it ; but in the absence of enlarged details of 
the pinnule segmentation, a critical comparison can scarcely be made. 

I have distinguished my example as Sphenopteris tenuifolia, Gutbier 
(? Brongt.), till the true relationship of these plants to each other is decided. 

Locality : — Upper Conygre Pit. 

Sphenopteris geniculata, Germar and Kaulfuss. 
Plate XXI. fig. 1. 

Sphenopteris geniculata, Germar and Kaulfuss, Verhandl. d. K. Leop. Carol. Akad. d. Naturf., 

vol. xv. part ii. p. 224, pi. lxv. fig. 2, 1831. 
Diplothmema geniculatum, Stur (in part), Carbon-Flora, p. 297, pi. xxxv. fig. 1. 
Sphenopteris Kaulfussi, Schimper, Traite d. paleont. veget., vol. i. p. 412. 

Description. — Primary (?) pinnae divided into two symmetrical portions ; 
rachis flexuous, winged ; secondary (?) pinnae alternate, lanceolate ; pinnules 

* Vers. d. Rothliegenden in Sachsen, p. 9, pi. ii. figs. 3, 4, 5. 

t Die Carbon- Flora der Schatzlarer Schichten, p. 257, pi. xxxi. fig. 5, 1885. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 347 

alternate, the lower divided into numerous simple or bifid linear acute seg- 
ments, into each of which runs a vein ; upper pinnules less divided, and may 
consist of only one or two bifid segments. 

Remarks. — The only British specimen of this rare species which I have 
seen is that figured on PI. XXI. fig. 1. It shows very beautifully the peculiar 
dichotomisation of the pinnse as developed on many Sphenopterids. The general 
outline of the pinnse is more or less subrotund, — that of its two component 
parts oval. The stalk uniting this compound pinna to the rachis is not pre- 
served, but was probably naked like that of the other members of this group 
of Sphenopteroids. 

Two of the pinnules are enlarged at fig. la.b. Throughout their segmenta- 
tion there can generally be traced a series of dichotomous divisions ; this 
is exhibited in both enlargements, where each of the two larger segments 
dichotomises. 

Both the primary (?) and secondary (?) rachis are distinctly winged and 
geniculate. 

Sphenopteris geniculata appears to have been much confused with Sphen. 
furcata, Brongt., and, following Geinitz, I united them in my Catalogue of 
Palaeozoic Plants, but now regard the two species as essentially distinct. 

Of the two figures of Sphen. geniculata given by Stur in his Carbon-Flora, 
that on his pi. xxxv. fig. 1, is evidently Germar and Kaulfuss' plant, but I 
think that on his pi. xxviii. fig. 1, is referable to Sphen. furcata. I believe 
also that the figure given by Geinitz as Sphen. geniculata * (which he unites 
with Sphen. furcata, Brongt.) must be excluded from Germar and Kaulfuss' 
plant. 

Locality : — Kilmersdon Pit. 

Sphenopteris Grandini, Goppert, sp. 

Sphenopteris Grandini, Schimper, Traite d. paleont. veget., vol. i. p. 404. 
Sphenopteris Grandini, Boulay, Terr, houil. du nord de la France, p. 27. 
Hymenophyllites Grandini, Goppert, Syst. fil. foss., p. 255, pi. xv. fig. 12. 
Sphenopteris alata, Brongt., Hist. d. veget. foss., p. 180, pi. xlviii. fig. 4. 
Sphenopteris alata, Sauveur, Veget. foss. de la Belgique, pi. xvii. fig. 2. 

Sphenopteris alata, Gutbier, Vers. d. Zwick. Schioarzkohl, p. 34, pi. v. figs. 16 and 17; pi. xi. 
% L 

Remarks. — This species is rare in the Eadstock Coal Field, but has been 
observed at several collieries. 

Stur unites Sphen. trichomanoides, Brongt, with Sphen. Grandini t (Sphen. 
alata, Brongt.). On the other hand, it is suggested by Boulay \ that Sphen. 

* Vers. d. Steinkf. in Sachsen, pi. xxiv. fig. 13. 

f Carbon-Flora d. Schatzlarer SchicMen, p. 304, 1885. 

% Loc. cit., p. 27. 



348 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

trichomanoides is simply a pinna of Sphen. furcata, Brongt., and Zeiller, though 
he includes Sphen. trichomanoides in his " Fougeres du terrain houiller du nord 
de la France,* is inclined to accept Boulay's suggestion. 

The specimens from Radstock are similar to Brongniart's type figure. 

Sphen. Grandini appears to me a very distinct plant, though, according to- 
Boulay, even it may be only a variety of Sphen. furcata, Brongt. This latter 
species has not yet been observed in the Radstock area, where Sphen. Grandini, 
though rare, is widely distributed. 

The ferns figured by Geinitz and Lesquereux as Brongniart's plant 
belong to another species.t 

Localities : — Eadstock ; Braysdown ; Lower Conygre. 



Sphenopteris macilenta, L. & H. 

Sphenopteris macilenta, L. & H., Fossil Flora, vol. ii. pi. cli. 

Sphenopteris macilenta, Geinitz, Vers. d. Steinkf. in Sachsen, p. 14, pi. xxiii. fig. 1. 
Sphenopteris macilenta, Zeiller, Bull, de la soc. geol. de France, 3 e ser. vol. xii. p. 194. 
Bphenopteris lobata, Gutbier, Vers. d. Zurich. Schwarzkold, p. 44, pi. v. figs. 11, 13, 14, 15 ; pi. x. 
figs. 1-3. 

Remarks. — Of very unfrequent occurrence. 

Dr Stur is evidently in error in separating Geinitz's and Gutbier's figures 
from Sphen. macilenta, L. & H., — a species in which the pinnule cutting 
varies much according to the position the pinnae hold on the frond.J 

Localities : — Radstock ; Braysdown ; Camerton. 



Sphenopteris Woodwardii, Kidston, n.s. 
Plate XIX. fig. 1. 

Description. — Frond tripinnate ; rachis very stout ; primary pinnae sub- 
opposite, ascending; secondary pinnae alternate or subopposite, lanceolate, 
ascending ; pinnules alternate, oblong-lanceolate, pinnatifid, rarely divided into 
lobes ; veins distinct, veinlets usually simple, occasionally bifid, — especially in 
those pinnules which are divided into lobes. 

Remarks. — The specimen figured is the only example of this species with 
which I have met. It was collected on one of my earlier visits to Camerton, 
and though diligent search has since been made for additional specimens I 
have not yet succeeded in securing any. 

The pinnules are most commonly merely pinnatifid, as shown at fig. la. 
The limb of the pinnules is of very delicate texture, but the veins are thick 

* Bull, de la8oc. geol. de France, 3 air., vol. xii. p. 194, 1883 

f See Kidston, Catal. I'alceoz. Plants, p. 78. 

t Carbon-Flora, p. 375 {Diplothmema macilentuiu). 



RADSTOCK SERIES OE THE SOMERSET AND BRISTOL COAL EIELD. 349 

and prominent, being raised like threads on the surface of the pinnule. The 
veinlets are usually simple, but where the pinnules show a tendency to become 
lobed they are bifid, as seen in the lower lobe of fig. lb. When the pinnules 
are divided into lobes, the vein in each lobe usually bifurcates, as shown in 
fig. lc. These lobed pinnules are of somewhat irregular occurrence on the 
pinnae. At the points marked x and x', where examples of these lobed pinnules 
occur, that at x is situated on a basal secondary pinna, whereas that at x' is on 
a secondary pinna, placed well up a primary pinna. On the same primary 
pinna the majority of the pinnules, even on secondary pinnae borne lower 
down on the rachis, are only pinnatifid, as seen at z and on the other pinnae 
of the specimen. 

The main rachis and those of the primary pinnae are very stout, as com- 
pared with those of the secondary pinnae ; they are feebly striated, and bear 
slightly elevated points. . 

The only species to which the Camerton plant appears to have any re- 
semblance are Sphenopteris (Cheilantheites) grypophylla, Goppert,* and Sphen. 
bidentata, Gutbier.t 

From Sphen. grypophylla, Sphen. Woodivardii is easily distinguished by its 
lanceolate, upward-directed pinnae, and the pinnatifid pinnules. In Sphen. 
grypophylla the pinnae are long and linear, and spring from the rachis at almost 
right angles, and the pinnules are uniformly divided into bifid lobes. In 
addition, the whole general appearance of the two plants is characteristically 
distinct. 

The type figure of Sphen. bidentata, Gutbier, is very fragmentary, and, 
except from the enlarged figure of the pinnule, a comparison of the species 
with any other is almost impossible. This enlarged pinnule shows a sharply 
bifid-toothed, spinous-like fern, which, both in the form of the pinnule and its 
segmentation, is essentially distinct from my plant. 

I have great pleasure in naming this specimen after Dr Henry Woodward, 
F.R.S., of the British Museum. 

Locality : — Camerton. 

Sphenopteris neuropteroides, Boulay, sp. 

Sphenopteris neuropteroides, Zeiller, Bull, de la soc. geol. de France, 3 e s^r., vol. xii. p. 191, 1883. 
Pecopteris neuropteroides, Boulay, Le terr. liouil. du nord de la France, p. 32, pi. ii. figs. 6 and 

6 Us, 1876. 
Pseudopecopteris anceps, Lesqx., Coal Flora of Pennsyl., vol. i. p. 207, pi. xxxviii. figs. 1-4, 1880. 

Remains. — Rare. I have compared a specimen of Pseudopecopteris anceps, 
Lesqx., from Pittston, communicated to Mr W. Cash, Halifax, by Mr R. D. 

* Syst.fil. foss., p. 242, pi. xxxvi. figs. 1, 2. See also Stur, Sphenopteris (Saccopteris) grypophylla, 
■ Carbon-Flora, p. 176, pi. liii. figs. 3, 4, 5. 

f Geinitz, Vers. d. Steinkf. in Sachsen, p. 16, pi. xxiv. fig. 3. 



350 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Lacoe,. with the examples of Sphen. neuropteroides from Somerset, and find, as 
suspected by Zeiller, that Pseudopecopteris anceps is identical with Sphen. 
neuropteroides, with which species it must therefore be united. 

It is interesting to note that the British, as well as the American and 
French, specimens of this fern appear to be infested with a species of 
Excipulites. 

Localities : — Radstock ; Camerton ; Withy ; Clandown. 

Sphenopteris cristata, Brongt., sp. 

Sphenopteris cristata, Schimper, Traite d. paleont. veget, vol. i. p. 397. 

Sphenopteris cristata, Kidston, Catal. Palwoz. Plants, p. 74. 

Pecopteris cristata, Brongt., Hist. d. veget. foss., p. 356, pi. cxxv. figs. 4, 5. 

Remarks. — The only specimen of this species with which I have met is that 
contained in the collection of the British Museum. 
Locality : — Camerton. 

Ptychocarpus, Weiss, 1869, Foss. Flora d. jiingst. Stk u. d. Rothl, p. 94. 

Description. — " Sori round or oval, divided by a longitudinal cleft into two 
oblong halves." 

Remarks. — The fruit of the genus Ptychocarpus appears to consist of two 
sporangia lying side by side. The systematic position of the genus is near to 
Asterocarpus ( = Pecopteris), but is separated from it by the sporangia being 
arranged in pairs, whereas in the Aster ocarpus-Pecopteroids the fruit is com- 
posed of several stellately arranged sporangia. In the type of Ptychocarpus 
(P. hexastichus) the sporangia are surrounded by a narrow flat border, from 
which Weiss thinks that the two sporangia were covered by an indusium, 
which, springing from the centre of the medial line, extended over and beyond 
the sporangia. 

He compares his genus Ptychocarpus to Didymochloena, Desv., and the 
external resemblance of the upper surface of the fruiting pinnules of Didymoch- 
lama sinuosa, as figured by Bauer,* to the species about to be described (P. 
oblongus) is very striking. In pointing out this external resemblance I do not 
at all infer any affinity between the recent and fossil genera. 

Ptychocarpus oblongus, Kidston, n. sp. 
Plate XX. fig. 2. 

Description. — Frond tripinnate (?); pinnae subopposite, lanceolate ; pinnules 
subopposite, oblong, usually bearing four pairs of oblong lateral lobes and a 
terminal one. On each lobe is situated an oblong synangium (?), composed of 

* Bauer and Hooker, Genera Filicum, or Illustrations of the Ferns and their other Allied Genera,. 
tahlc viii. figs. 2, 3. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 351 

two sporangia (?). The main rachis and those of the pinnae are stout, and pitted 
with scale-scars. 

Remarks. — It is with considerable reservation that I place this species in 
the genus Ptychocarpus, Weiss. 

The general appearance of my specimen exhibits a great similarity to Weiss' 
genus, but, on minute examination, I cannot positively affirm that the longi- 
tudinal cleft entirely divides the two supposed sporangia, as it does in P. 
hexastichus, Weiss (loc. cit., pi. xi. fig. 2). The usual appearance of the fruit of 
the Camerton plant is shown at Plate XX. figs. 2a and b ; at fig. 2b the cleft is 
seen to be much more prominent in the central part than at the two extremities, 
where it becomes indistinct. This may be merely caused by imperfect preserva- 
tion, or even by the degree of maturity at which the specimen had arrived when 
embedded. This supposed bi-sporangial synangium is generally surrounded by 
a faint border, as shown at figs. 2a and b, which appears as a slight surrounding 
staining, but is clearly observable in many cases. 

The pinnules seem to have been divided into lobes, on each of which was 
borne a (?) synangium. I am disposed to think that this surrounding border 
may not represent an indusium, but the margin of the limb of the pinnule 
on which the sporangia sat. The fruit seems to have had a firm consistency, 
and has still considerable elevation. 

On collecting this fossil, my first impression was that each segment of the 
pinnules bore a split exannulate sporangium, but, as a result of further examina- 
tion and comparison with the description of Ptychocarpus, Weiss, I have pro- 
visionally placed it in that genus. 

The only example met with is that figured. 

Locality : — Camerton. 

Schizostachys, Grand' Eury, 1877, Flore carbon du Departement de la 

Loire, §c, p. 200. 

Remarks. — This genus is characterised by its oblong, slightly curved, pedi- 
cellate sporangia, attached around a common point, or on the sides of a short 
pedicel. In the species described by Grand' Eury* the cellular tissue of the 
sporangia was still visible ; some of these cells were especially prominent, and 
formed a band which encircled the sporangium. This band may perhaps repre- 
sent an annulus. On the surface of the sporangia is a longitudinal line, to 
which these (?) annulus-forming cells seem to lie at a right angle. 

Grand' Eury regarded his Schizostachys frondosus as the male inflorescence 
of Noeggerathia ; Renault, on the other hand, places it among the ferns,t and 
this appears to be its true position. 

* Schizostachys frondosus ; on his pi. xvii. fig. 3, named Androstachys frondosus. 
f Cours d. botan. foss., Troisieme Ann^e, 1883, p. 103. 
VOL. XXXIII. PART II. 3 G 



352 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Renault has further suggested that the fruit described by Grand' Eury as 
Schizostachys may perhaps be identical with that described by him as the fruit 
of Zygopteris* 

In the whole mode of its growth Schizostachys ramosus, Gr.' E., approaches 
so closely to Schizopteris pinnata, Gr.' E., and S. cycadina, Gr.' E., that it 
induces the supposition that it might be the fruit of one of these, or of a closely 
allied species. 

As, however, the fruiting specimens show no barren foliage, they cannot be 
referred to these ferns with any degree of certainty. 

Schizostachys sphenopteroides, Kidston, n. sp. 
Plate XX. fig. 1. 

Description. — Frond bipinnate ; pinnae subopposite, linear, lanceolate ; pin- 
nules subopposite, coriaceous, and composed of one sporangium on the upper 
pinnae, and of two diverging sporangia on the lower pinnae. Sporangia oblong, 
with a central line, from which extends a series of transverse bars. Rachis 
faintly striated. 

Remarks. — A specimen is shown on Plate XX. fig. 1, natural size. The 
pinnules, which are quite destitute of any leafy expansion, are reduced to one 
or two sporangia, according to their position on the frond. The sporangia are 
oblong and straight, or very slightly curved. On their surface is a longitudinal 
line, from which the little transverse bars extend at right angles. The specimen 
is not sufficiently well preserved to exhibit the cellular structure of the spor- 
angia, as in the case of that described by Grand' Eury, but it shows the trans- 
verse bars as drawn at fig. la. These bars extend over almost the whole of 
the exposed surface of the sporangia, but that they indicate the presence of an 
annulus I am unable to determine. 

I apply the specific name of sphenopteroides to this species from its super- 
ficial resemblance to some of the members of that genus. 

Locality : — Eadstock. 

Macrosphenopteris, Kidston, n. gen. 

Descrij)tion. — Pinnules very large, ovate, of delicate texture, provided with 
a central vein, from which spring numerous upward-directed dichotomous 
veinlets. Margin dentate or laciniate. 

Remarks. — This genus is proposed for the Adiantites Haidingsri, Ettings- 
hausen,t and the specimen about to be described. 

* Lor,, cit, p. 102. 

f Die Steinkohlenfora von Radniiz, p. 34, p], xix, fig. 3. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 353 

The genus Adiantites, Goppert, as originally employed by its author, bad a 
very vague significance, and in it were placed ferns of very different character. 
The genus has been emended by Schimper,* and as now defined, Adiantites 
Haidingeri, Ett., can no longer be included in it. It is therefore necessary to 
create a new genus for this fern and for the one I now describe as Macro- 
sphenopteris Lindsceoides. 

The remains of these ferns are treated as pinnules, as their general appear- 
ance points to this conclusion rather than to their being fronds. 

Macrosphenopteris, in the delicate texture of the pinnules and the arrange- 
ment of the veins, shows affinities with Sphenopteris, hence the name (Macro- 
sphenopteris) now proposed for it. 

Macrosphenopteris Lindsseoid.es, Kidston, n. sp. 
Plate XXVII. fig. 1. 

Description. — Pinnules very large, of delicate texture, with a central vein, 
from which arise numerous ascending slightly curved dichotomous veinlets. 
Margin sinuous or dentate. 

Remarks. — The specimen figured is the only example met with. It is 
unfortunately very imperfect, but the portion preserved shows that the 
pinnule must have been of large size. Its texture is very delicate, and the veins 
are distinct. At several parts of the pinnule the margin is thickened in a very 
peculiar manner ; whether this is caused by a folding over of the margin or a 
thickening of the tissue at this part of the pinnule, cannot be determined. The 
appearance is not accidental, and is possibly connected with the fructification 
of the species ; it has a strong superficial resemblance to the arrangement of 
the indusia of the genus Lirtdswa, which has suggested the specific name of 
Lindsazoides. 

Macrosphenopteris Lindsasoides, though closely related to Macrosphenopteris 
Haidingeri, Ett., sp., appears to have been a much larger species, with more 
distant nervation, and the margin not regularly dentate as in Ettingshausen's 
plant, where each of the veinlets seems to end in a small tooth. 

The Aphlebia pateriformis, Germar,t may be allied to Macrosphenopteris, but 
" a distinct dichotomy of the longitudinal stripes (veins ?) is not recognisable " 
in Germar's plant. 

Locality : — Had stock. 

* Traite d. paleont. veget., vol. i. p. 424 (Adiantides). 

f Vers. de. Steink. v. Wettin u. Lobejun, fasc. 1, p. 5, pi. ii. 



354 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Neuropteris, Brongniart, 1822, Sur la Classification des tegetaux fossiles, p. 33. 

Neuropteris macrophylla, Brongt. 
Plate XXI. fig. 2; Plate XXII. figs. 2, 3. 

Neuropteris macrophylla, Brongt., Hist. d. veget. foss., p. 235, pi. lxv. fig. 1. 

Neuropteris macrophylla, Schimper, Traite d. paleont. veget., vol. i. p. 434. 

Neuropteris Clarksoni, Lesqx., in Roger's Geol. of Pennsyl., vol. ii. p. 857, pi. vi. figs. 1-4. 

Neuropteris GlarTisoni, Coal Flora of Pennsyl., p. 94, pi. ix. figs. 1-6. 

Neuropteris Scheuchzeri, Kidston (not Hoffm.), Catal. of Pal&oz. Plants, p. 95. 

(?) Osmunda, Scheuchzer, Herbarium diluvianum, p. 48, pi. x. fig. 3, edition 1709. 

Description. — Frond very large ; pinnae dividing by a series of dichotomies. 
Pinnules alternate, varying much in shape and size, triangular, lanceolate- 
acute, oblong-obtuse, and cyclopteroid. Midrib distinct, and extending to the 
apex ; lateral veins numerous, arched, generally dichotomising four times, 
rarely five times, the last dichotomy being near the margin of the pinnule. 
Veins reaching the edge of the pinnule at an open angle. The cyclopteroid 
pinnules are situated on the rachis. 

Remarks. — Neuropteris macrophylla was described by Brongniart from a 
specimen collected at Dunkerton, Somerset, which belonged to the Geological 
Society of London, and in whose collection it still remains. The species is 
frequent in the Radstock Coal Field, from which some large and fine specimens 
have been secured. 

Having compared my specimens with the type, I am satisfied of their 
identity with it. This comparison was necessary as Brongniart's repre- 
sentation of the nervation of his type is too coarse and distant. In fact, the 
nervation of Neuropteris macrophylla is much more like the nervation of Neur. 
auriculata as represented by Brongniart on his plate lvi. fig. a, than it is to 
the enlarged drawing that accompanies the original figure of the species. This 
led me to conclude that these two species were identical, but Zeiller, to whom 
I sent specimens of Neur. macrophylla, kindly compared them with the type of 
Neur. auriculata, and informed me that Neur. auriculata has a much closer 
nervation than Neur. macrophylla, and the apex of the pinnules of Neur. 
auriculata is rounded. As the nervation forms a constant character for dis- 
tinguishing the species of the genus Neuropteris, Neur. auriculata cannot be 
united with Neur. macrophylla. The form of the pinnules, at least in the 
present case, seems of little specific value. A figure is given on Plate XXII. fig. 
3, of a specimen from Radstock in the Bath Museum. On the left side of the 
rachis the pinnules are oval, and very blunt, whereas on the right they are lanceo- 
late. These differences are very clearly exhibited towards the apex of the fossil. 

The posterior basal angle of the pinnules is usually more or less auricled. 
The various forms assumed by the pinnules of this species will be best appre- 
ciated by an examination of the three figures that accompany these notes. To 
Plate XXII. fig. 3, reference has already been made ; at fig. 2 of the same plate 



RADSTOCK SERIES OE THE SOMERSET AND BRISTOL COAL FIELD. 355 

a fragment of a pinna is given, which, in addition to showing lanceolate pinnules, 
exhibits the dichotomous ramification of the rachis. The pinnules situated 
at the angles formed by the dichotomies are of very irregular shape, being 
frequently triangular and irregular, sometimes even bifid at their apex, as if two 
pinnules had become confluent. The most interesting specimen I figure is that 
on PI. XXI. fig. 2. On this example (which lies on the corner of a very large 
slab of Neur. macrophylla, which I received from Mr Steart, manager of the 
Braysdown Colliery), the gradual transition in the form of the pinnules from 
lanceolate to cyclopteroid can be followed. On some specimens in the col- 
lection of Mr J. M'Murtrie, F.G.S., large cyclopteroid pinnules occur on a 
thick rachis, which may be the main rachis of the frond. 

From Neur. Scheuchzeri, Hoffm., this species is easily distinguished by the 
absence of the small cyclopteroid pinnules at the base of the large terminal 
lobe, by its being destitute of the bristle-like hairs, and, above all, by its 
nervation. In Neur. macrophylla the ultimate dichotomy of the veins is much 
closer to the margin of the pinnule than the corresponding dichotomy in Neur. 
Scheuchzeri, and in the latter species the veins are closer. 

From the figure of Neur. Scheuchzeri given by Zeiller (loc. cit., pi. xli. fig. 1), 
it appears that this species possesses a similar dichotomous ramification of the 
pinnae to that which maintains in Neur. macrophylla. 

Through the kindness of Mr C. Cash, F.G.S., Halifax, Yorkshire, I have 
been able to compare with my specimens of Neur. macrophylla a specimen of 
Neur. Clarksoni, Lesqx., from Olyphant, which was communicated to him by 
Mr R. D. Lacoe, and find this last mentioned species is specifically identical 
with Brongniart's plant. 

I am inclined to refer the figure given by Scheuchzer (loc. cit., pi. x. fig. 3) 
to Neur. macrophylla, Brongtrr~though several writers have placed it under 
Neur. Scheuchzeri, Hoffm. From the roughness of Scheuchzer's figure, it is 
impossible definitely to refer it to either of these species. 

While writing my Catalogue of Palseozoic Plants in the British Museum, 
believing that Scheuchzer's figure should be referred to Hoffmann's Neur. 
Scheuchzeri (which, however, I treated as distinct from Neur. cor data, L. & H. = 
Neur. hirsuta, Lesqx.), I identified in error the specimens of Neur. macrophylla 
as Neur. Scheuchzeri, Hoffm. 

The inaccurate drawing of the nervation of Brongniart's type of Neur. 
macrophylla prevented me from identifying the specimens in the British Museum 
with his plant, to which, however, they really belong, and it was only on a 
subsequent examination of the specimens in the collection of the Geological 
Society of London that I detected the type of Neur. macrophylla, which enabled 
me to discover my former error. 

Localities: — Dunkerton (Type); Wellsway; Radstock; Upper Conygre; 
Lower Conygre; Braysdown; Kilmersdon. 



356 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Neuropteris Scheuchzeri, Hoffmann. 
Plate XXIII. figs. 1, 2. 

Neuropteris Scheuchzeri, Hoffni., Keferstein's Tcuchland geognostisch-geologisch dargestellt., vol. iv. 

p. 156, pi. lb, figs. 1-4, 1826. 
Neuropteris Scheuchzeri, Zeiller, " Flore Houillere d. Asturies," p. 10 (Mem. Soc. Geol. du Nord, 

1882). 
Neuropteris Scheuchzeri, Zeiller, Qites Mineraux de la France. Descrip. de la Flore Foss. Bassin 

houil. d. Valenciennes, pi. xli. figs. 1-3, 1886. 
Neuropteris angustifolia, Brongt., Hist. d. veget. foss., p. 231, pi. lxiv. figs. 3-4. 
Neuropteris acutifolia, Brongt., Hist. d. veget. foss., p. 231, pi. lxiv. figs. 6, 7. 
Neuropteris acutifolia, Ettingshausen, Foss. Flora v. Radnitz, p. 32, pi. xviii. fig. 5. 
Neuropteris acutifolia, Geinitz, Vers. d. Steinlf. in Sachsen, p. 22, pi. xxvii. fig. 8. 
Neuropteris acutifolia, Gutbier, Vers. d. Ziuiclc. Schiuarzlcohl, p. 52, pi. vii. fig. 6. 
Neuropteris cordata (not Brongniart), Bunbury, Quart. Jour. Geol. Soc, vol. iii. p. 423, pL xxi. 

fig. 1, a-f 
Neuropteris cordata, Gb'ppert, Foss. Flora d. perm. Form., p. 100, pi. xi. figs. 1, 2. 
Neuropteris cordata, Lindley & Hutton, Foss. Flora, vol. i. pi. xli. 
Neuropteris cordata, Kidston, Catalogue of Palaeozoic Plants, p. 98. 

Neuropteris hirsuta, Lesquereux, Rep. Geol. Survey of Illin., vol. ii. p. 427, pi. xxxv. figs. 6-10. 
Neuropteris hirsuta, Lesquereux, Coal Flora of Pennsyl., p. 88, pi. viii. figs. 1, 4, 5, 7, 9, 12. 
Dictyopteris cordata, Rorner, Palmontographica, vol. ix. p. 30, pi. vi. fig. 4, 1862. 
Dictyopteris Scheuchzeri, Romer, Palteontographica, vol. ix. p. 30, pi. ix. fig. 1, 1862. 

Description. — Frond large, ultimate pinnae alternate, lanceolate, and usually 
composed of a large terminal and two small cyclopteroid pinnules ; medial 
vein extending to within a very short distance of the apex, lateral veins fine, 
close, numerous, usually divided four times, — the fourth dichotomy occurring 
about midway between the midrib and the margin, and reaching the edge of 
the pinnule at a wide angle. The surface of the pinnules bears irregularly 
scattered short bristle-like hairs. Large cyclopteroid pinnules are also present 
on the frond. 

Remarks. — The specimen I figure, which is in the collection of the Bath 
Museum, shows a fragment of what must have been a very large frond. At the 
top of the specimen the pinnae are reduced to a large pinnule with a basal lobe. 
The other pinna? consist of a very large terminal pinnule, at the base of which, 
on each side of the rachis, is a small cyclopteroid pinnule. The terminal pinnule 
marked xis, 8 cm. long, but the one immediately below it must have been larger. 

Probably no species of the Carboniferous flora has been so much misunder- 
stood and misidentified as Neur. Scheuchzeri, Hoffm. This arises from the 
imperfect figures and description of the type specimens, to which may be added 
the difficulty in obtaining the work in which the original description appears. 

We are chiefly indebted to Zeiller for unravelling the synonymy of this 
species. 

Neur. Scheuchzeri has, in the great majority of cases, been identified in error 
as Neur. cordata, Brongt."" 

* Hist. d. veget. foss., p. 229, pi. lxiv. fig. 5. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 357 

Of Neur. cordata, Brongniart only figured a single pinnule, which in its 
form closely resembles the pinnules of Neur. Scheuchzeri. The type of Neur. 
cordata appears to be lost, but Zeiller has discovered in the Museum at Paris 
many other specimens named Neur. cordata by Brongniart himself; these, 
however, embrace two species. Some of them are the true Neur. cordata as 
figured by Brongniart and others, are identical with the plants named Neur. 
acutifolia, Brongt., and Neur. angustifolia, Brongt. Zeiller has very kindly 
sent me a specimen from the mines of Alais, Grand' Combe, of the plant he 
identifies as the true Neur. cordata, Brongt. With this before me there is no 
difficulty in recognising Brongniart's Neur. cordata as essentially distinct from 
Neur. Scheuchzeri, with which, as will be presently seen, must be united Neur. 
acutifolia, Brongt., and Neur. angustifolia, Brongt. In Neur. cordata the veins 
are not nearly so close to each other as those of Neur. Scheuchzeri, and in 
addition to this the characteristic hairs of Neur. Scheuchzeri are absent from 
Neur. cordata; — even on specimens of Neur. Scheuchzeri where, through 
imperfect preservation, the hairs are not visible, the nervation is a sufficiently 
distinctive character by which to distinguish the two species. 

The nervation of Neur. Scheuchzeri, enlarged three times, is shown on 
Plate XXIII. fig. 2. The hairs are omitted from this figure to avoid confusion. 
It will be observed from this drawing that the veins usually divide four times, — 
the first dichotomy being close to the midrib, the second and third dichotomy 
carry the veins to about midway between the central vein and the margin of 
the pinnule, and the arms of the fourth dichotomy extend from this point to 
the edge of the pinnule. A fifth dichotomy is but rarely observed, and equally 
rarely do its veins only divide three times throughout their course. 

An enlarged drawing, to show the bristle-like hairs, is given at fig. la. 
These usually lie obliquely to the veins, imparting to the pinnule a dictyopteroid 
appearance, which has given rise to Romer's Dictyopteris cordata and Dicty- 
opteris Scheuchzeri. 

On the original specimens of Neur. Scheuchzeri the presence of the hairs 
appears to have escaped Hoffmann's observation, or had been effaced through 
imperfect preservation, but, from his description of the plant and the accom- 
panying figures, the identification of the specimens occurring in the Radstock 
Coal Field with Hoffmann's Neur. Scheuchzeri appears to be correct beyond 
doubt. 

Zeiller has examined the types of Neur. acutifolia and Neur. angustifolia 
which originated from "Camerton" and "near Bath," and "Wilkesbarre in 
Pennsylvania," and has observed on them the characteristic hairs, though 
Brongniart in his description of the two species does not indicate their exist- 
ence. These two supposed species do not differ from each other except in the 
outline of the pinnules, which is not of sufficient value for specific distinction, 



358 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

and, further, it has been shown by Zeiller that they are specifically identical 
with Neur. Scheuchzeri, Hoffm. 

Bunbury was the first to point out the presence of hairs on specimens of 
Neur. Scheuchzeri from Cape Breton, though he identified his plants as Neur. 
cordata* He also mentions that he had observed these little hairs on 
specimens of Neur. cordata, L. & H. (not Brongniart), from Leebotwood (the 
locality from which Lindley and Hutton's examples come), in the collection of 
the Geological Society of London, and this observation I am able to cor- 
roborate. 

Bunbury here also places Neur. angustifolia, Brongt., as a variety of Neur. 
cordata, and further suggests that Neur. cordata, New. angustifolia, Neur. 
acutifolia, and Neur. Scheuchzeri of Brongniart are all of them forms of Neur. 
cordata. 

LESQUEREUxt at one time expressed a similar belief, but subsequently he 
treated Neur. cordata, Neur. hirsuta, and Neur. angustifolia as distinct, giving 
Lindley and Hutton's figure as a reference under Neur. cordata, Brongt., but, 
as already stated, the specimens from Leebotwood belong to Neur. Scheuchzeri, 
and not to Neur. cordata, Brongt. X 

Neur. hirsuta, Lesq.,§ agrees in every respect with Neur. Scheuchzeri; 
Lesquereux's species, however, was created before the true characters of 
Neur. Scheuchzeri were clearly understood ; but it must now be reduced to a 
synonym of the latter-mentioned plant. 

Goppert gives a figure in his Permian Flora which he names Neur. cordata.\ 
This does not show the small cyclopteroid pinnules that are generally present, 
but the form of the large pinnules and their nervation, as shown by his enlarge- 
ment, agree entirely with Neur. Scheuchzeri, to which plant I believe his fern 
may belong. 

Zeiller, in his excellent remarks on Neur. Scheuchzeri, to which I am much 
indebted for a right understanding of this species, includes under Neur. 
Scheuchzeri the figure of a Neuropteris from England given by Scheuchzer in 
his Herbarium Deluvianum, pi. x. fig. 3 (edition 1709). It is impossible to 
speak definitely on the specific position of the fern figured by Scheuchzer, but 
I feel more inclined to identify it as Neur. macrophylla, Brongt., than Neur. 
Scheuchzeri, Hoffm. 

While preparing the Catalogue of the Palaeozoic Plants in the British 
Museum, with only figures and descriptions of these species before me, and all 

* Quart. Jour. Geol. Sue, vol. iii. p. 424, 1847. 
t In Roger's Geol. of Penneyl., vol. ii. part 2, p. 857, 1858. 

J The nervation of Lindley and Hutton's figures is very diagrammatic, and by no means represents 
the correct nervation of the plant they figure. 

§ Coal Flora of Pennsyl, pp. 88, 89, 91, 1880. 
|| PI. xL fig. 1. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 359 

of them, with one exception, misidentifications, I now find that the plants I 
there placed under Nenr. cor data, L. & H. (?Brongt.), # should be referred to 
Neur. Scheuchzeri, HofFm., and the ferns I placed under Neur. Scheuchzeri must- 
be referred to Neur. macrophylla, Brongt. Further remarks will be found on 
this subject under Neur. macrophylla, Brongt. 

My thanks are due to the Rev. H. H. Winwood, F.G.S., for facilities given 
for figuring the fine specimen shown on PI. XXIII. fig. 1. 

Neur. Scheuchzeri occurs in several of the English coal fields. 

Localities : — Braysdown ; Radstock ; Upper Conygre ; Lower Conygre ; 
Camerton ; Wellsway. 

Neuropteris flexuosa, Sternberg. 

Neuropteris flexuosa, Sternb., Vers., i. fasc. iv. p. xvi. 

Neuropteris flexuosa, Brongt., Hist. d. veget. foss., p. 239, pi. lxviii. fig. 2 ; pi. lxv. figs. 2, 3. 

Neuropteris flexuosa, Schimper, Traite d. paleont. veget., vol. i. p. 434, pi. xxx. figs. 12, 13. 

Neuropteris flexuosa, Kidston, Catal. Palteoz. Plants, p. 93. 

Osmunda gigantea, var. /?, Sternb., Vers., i. pp. 36 and 39, pi. xxxii. fig. 2. 

Neuropteris plicata, Lesqx., Goal Flora of Pennsyl., pi. x. figs. 1-4. 

Remarks. — Frequent. The plants figured as Neuropteris plicata by Les- 
QUEREUX,t seem clearly referable to Neur. flexuosa, Sternb., whatever may be 
the true value of Sternberg's species.! 

Var. rotundifolia. 

Neuropteris rotundifolia, Brongt., Hist. d. veget. foss., p. 238, pi. lxx. fig. 1. 
Neuropteris rotundifolia, Gutbier, Vers. d. Zwick. Schwarzkohl, p. 56, pi. vii. figs. 3, 4. 

Remarks. — This form has beeli found at Camerton, but it passes into Neur. 
flexuosa, of which it can only be regarded as a varietal form. 

Localities : — Radstock ; Camerton ; Upper Conygre ; Lower Conygre. 

Neuropteris ovata, Hoffmann. 
Plate XXII. fig. 1. 

Neuropteris ovata, Hoffmann, Keferstein's Teuchland geognostisch-geologiscli dargestellt, vol. iv. p. 
158, pi. lb, figs. 5, 6, 7 (excl. fig. 8), 1826. 

Description. — Frond much divided ; rachis of primary pinnae broad and 
finely striated ; secondary pinnae subopposite ; rachis stout ; pinnules alternate, 
oblong, apex rounded, superior basal angle rounded and sloping inwards, 
inferior angle produced as a rounded auricle. Veins fine, close, arched, 

* Tbe true Neuropteris cordata has not yet, as far as I am aware, been discovered in Great Britain. 

t N. plicata, Lesqx., Coal Flora, loc. cit. 

X Vers., i. fasc. 4, p. xvi. ; ii. p. 74, pi. xix. figs. 1-3. 

VOL. XXXIII. PART II. 3 H 



360 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

usually divided four times, and meeting the margin of the pinnule at an 
acute angle. Midrib, strictly speaking, absent. Terminal lobe but little 
enlarged, broadly lanceolate, and generally confluent with uppermost pinnule 
or pinnules. 

Remarks. — The specimens I identify as Hoffmann's plant agree in all 
respects with the figures and description given by him. 

Neur. ovata has a great similarity in general appearance to Neur. Jiexuosa, 
Sternb., but is distinguished from it by constant and well-marked characters. 
Both species occur in the Radstock Coal Field ; Neur. Jiexuosa is of frequent 
occurrence, but Neur. ovata is scarcely so common. 

The terminal pinnule in Neur. ovata is never enlarged as in Neur. Jiexuosa. 
It is usually more or less broadly lanceolate, and at its basal extremity is con- 
nected with the uppermost pinnule or pinnules. The pinnules are auricled in 
a manner similar to those of Neur. Jiexuosa, but they do not overlap so much 
as in the latter-mentioned species. The veins are more arched than in Neur. 
Jiexuosa, and also appear to be more numerous. 

A few of the upper pinnules are attached by their whole base to the rachis ; 
the others are articulated by a short, almost imperceptible footstalk. A care- 
fully enlarged drawing of a pinnule to show the nervation is given at fig. la. A 
true midrib can scarcely be said to be present. One or two veins, springing 
from the base of the pinnule, lie almost parallel, but, before reaching the apex, 
are lost in repeated dichotomies. 

I have excluded from Hoffmann's reference his fig. 8, as there is really no 
evidence to show that this figure belongs to Neur. ovata, and much less that it 
should be regarded as the fruit of that species.* 

Heer appears to have included under Neur. Jiexuosa more than one species 
of Neurojpteris.^ Some of his figures, I believe, should be referred to Neur. 
ovata {of. pi. ii. fig. 2 ; pi. iii. fig. 2, &c). 

As neither the figure nor the description of the plant given by Romer as 
Neur. ovata agrees very well with Hoffmann's figures or description, I am 
doubtful of the correctness of Romer's identification.! 

Neur. ovata is liable to be mistaken for a small form of Neur. Jiexuosa, but 
a comparison of well-preserved specimens of the two species will, I believe, at 
once show their specific individuality. 

At fig. 1, Plate XXII., are given some pinnae of Neur. ovata, drawn natural 
size. 

Localities : — Upper Conygre ; Camerton ; Radstock ; Wellsway. 

* See Kidston, Trans. Roy. Soc. Edin., vol. xxxiii. pt. i. p. 150, 1887. 
f Flora fow. Helvetia, p. 20, pis. ii. figs. 1-7 ; iii. 1-5; iv. 7-13; v. 2, 3. 
X PalceontograpTiica, voL ix. p. 28, pi. vi. fig. 1. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 3(31 



Neuropteris rarinervis, Bunbury. 

Neuropteris rarinervis, Bunbury, Quart. Jour. Geol. Soc, vol. iii. p. 425, pi. xxii. 
Neuropteris rarinervis, Lesqx., Goal Flora of Pennsyl., p. 109, pi. xv. figs. 2-5. 
Neuropteris rarinervis, Zeiller, Bull. soc. geol. de France, 3 e ser., vol. xii. p. 197. 
Neuropteris rarinervis, Kidston, Catal. Palceoz. Plants, p. 91. 

Remarks. — Though occurring at most of the localities visited, this fern is 
nowhere plentiful in the Raclstock Coal Field. 

Localities : — Kadstock ; Camerton ; Wellsway ; Upper Conygre ; Lower 
Conygre. 

Neuropteris flmbriata, Lesqx. 
Plate XXI. figs. 3-5. 

Neuropteris fimbriata, Lesqx., Geol. Report of Ulin., vol. ii. p. 430; vol. iv. p. 384, pi. vi. fig. 4. 
Neuropteris flmbriata, Lesqx., Coal Flora of Pennsyl., vol. i. p. 81, pi. v. figs. 1-6. 

Remarks. — A few isolated pinnules have been met with which may perhaps 
be referred to Neur. fimbriata, Lesqx. These are shown on PI. XXI. figs. 3-5. 

In the specimen given at fig. 5 the veins are a little finer than in those of 
figs. 3 and 4, and it may possibly be a small specimen of Neuropteris (Cyclopteris) 
lacerata, Heer.* 

The other two figures, however, appear to agree more closely with 
Lesquereux's Neur. fimbriata, but Heer's and Lesquereux's species ap- 
proach very closely to each other, and the distinctive characters are not very 
prominent. 

The fimbriation of the pinnules Js a natural character, and not produced by 
an accidental flaying out of the tissue. 

Localities : — Upper Conygre ; Camerton ; Wellsway. 

Dictyopteris, Gutbier, 1835. Abdrucke und Versteinerungen des Zwickauer 

Scliivarzkoldengebirges, p. 62. 

Dictyopteris Miinsteri, Eichwald, sp. 
Plate XXL fig. 6. 

Odontopteris Miinsteri, Eichwald, Die Urwelt Russlands, Heft i. p. 87, pi. iii. fig. 2, 1840. 

Dictyopteris Miinsteri, Schimper, Traite d. paleont. veget., vol. i. p. 618, 1869. 

DictyopAeris Miinsteri, Zeiller, Bidl. soc. geol. de France, 3 e ser., p. 197, vol. xii.; Etudes d. Gites 

Mineraux de la France ; Bassin houil. d. Valenciennes, Descr. d. I. Flore Foss., pi. xlix. 

figs. 1-5, 1886. 
Dictyopteris Hoffmanni, Romer, PalwontograpMca, vol. ix. p. 29, pi. vii. fig. 3, 1862. 
Dictyopteris Hoffmanni, Schimper, Traite d. paleont. veget., vol. i. p. 619. 

Description. — Frond tripinnate, secondary pinnae alternate, lanceolate; 
pinnules alternate, from shortly oval to oblong in form; upper pinnules united 

* Flora foss. Helvetia, p. 17, pi. vi. fig. 7. 



362 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

to the rachis by their whole base, lower attached by a short footstalk, arti- 
culated. Anterior basal angle of pinnule rounded, posterior basal angle slightly 
auricled. Medial vein flexuous, and extending almost to the apex. Lateral 
veins dividing several times, anastomosing, and forming an irregular 
network. Meshes next the midrib longer than those further removed from 
it. Terminal pinnule lanceolate. The frond also bears large cyclopteroid 
pinnules. 

Remarks. — I am indebted to Mr George West, Camerton, for the fine speci- 
men of this species shown on PI. XXI. fig. 6. From the inequality of the pinnae 
on opposite sides of the rachis, the example is evidently only a pinna. At the 
apex are several large simple lanceolate pinnules; on the third highest pinna 
of those preserved, on each side of the terminal pinnule are a pair of almost 
semicircular pinnules (fig. Qa x 3) attached to the rachis by their whole base. 
On the lower pinnse the pinnules are oblong, with occasionally slightly tapered 
apices. 

The veins form a very loose and irregular network. Those next the 
flexuous midrib are elongated in the longer direction of the pinnule, i.e., more 
or less parallel with the midrib. The meshes formed by the subsequent dicho- 
tomies of the veins are directed more upwards and outwards, and become 
smaller towards the margin of the pinnule. The reticulation is formed rather 
by a bending of the veins towards each other than by their actual union. 
The pinnules on the main figure are not so large as some shown at the 
part indicated by an x. Zeiller figures a cyclopteroid pinnule of this 
species (loc. cit., fig. 4). These were probably borne on the main rachis as in 
Neuropteris. 

A comparison of my example with Romer's Dictyopteris Hoffmanni leaves 
no doubt as to the identity of the two plants. But it seems equally clear that 
D. Hoffmanni, Romer, is only a more perfect specimen of D. Miinsteri, Eich., sp., 
and this opinion has already been indicated by Zeiller.* 

Through the kindness of Dr Weiss I have been enabled to compare a speci- 
men of J). Hoffmanni from Piesberg (the original locality of this species) with 
the Camerton plant; their nervation is similar, but in the size of the pinnules 
the Piesberg example agrees more with the figures of D. Miinsteri, as given by 
Zeiller, than the plant figured by me. 

The presence of the large terminal pinnule does not seem to be a constant 
character, for on some of the specimens of D. Miinsteri, figured by Zeiller, 
which agree exactly on their nervation with the specimen of I). Hoffmanni sent 
me by Dr Weiss, the terminal pinnules are comparatively small. 

Locality : — Camerton. 

* Bull. soc. rjeol. de France, 3 C ser., vol. xii. p. 197. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 363 

Odontopteris, Brongniart, 1822, Sur la classification des vegetanx fossiles, 

p. 34. 

Odontopteris Lindleyana, Sternb. 

Odontopteris Lindleyana, Sternb., Vers., ii. p. 78. 

Odontopteris obtusa, L. & H. (not Brongt.), Fossil Flora, vol. i. pi. xl. 

(?) Odontopteris heterophylla, Lesquereux, Geol. Rep>. of Illin., vol. ii. p. 433, pi. xxxviii. figs. 2, 5. 

(?) Odontopteris heterophylla, Coal Flora of Pennsyl., vol. i. p. 129, pi. xxii. fig. 6. 

Remarks. — The type of Lindley and Hutton's species is preserved in the 
University Museum, Oxford, but the figure given in the Fossil Flora is not a 
very correct representation of the specimen. 

Odontopteris Lindleyana is very rare in the Kadstock Coal Field, but occurs 
more plentifully in the shale over Pontydwaith Seam, Pochin Pit, near 
Tredegar, South Wales. The examination of the type and the additional 
specimens from Radstock and South Wales has shown that Lesquereux's 
Odontopteris heterophylla is probably identical with the plant figured in error 
by Lindley and Hutton as Odontopteris obtusa. 

Localities : — Radstock ; Braysdown. 

Mariopteris, Zeiller, 1879, Bidl. soc. geol. de France, 3 e ser., vol. vii. p. 92. 
Mariopteris nervosa, Brongt., sp. 

Mariopteris nervosa, Zeiller, Veget. foss. du. terr. houil., p. 69, pi. clxvii. figs. 1-4. 
Pecopteris nervosa, Brongt., Hist. d. veget. foss., p. 297, pi. xciv. ; pi. xcv. figs. 1, 2. 
Pecopteris nervosa, Lindley and Hutton, Fossil Flora, vol. ii. pi. xciv. 
Alethopteris nervosa, Geinitz, Vers. d. Steinlf. in Sachsen, p. 30, pi. xxxiii. figs. 2, 3. 
Pseudopecopteris nervosa, Lesqx., Coal Flora of Pennsyl., vol. i. p. 197, pi. xxxvi. figs. 1-3. 

Remarks. — Very rare. 

Localities : — Radstock ; Upper Conygre. 

Mariopteris muricata, Schlotheim, sp. 

Mariopteris muricata, Zeiller, Veget. foss. du terr. houil., p. 71, pi. clxvii. fig. 5. 
Pecopteris muricata, Brongt., Hist. d. veget. foss., p. 352, pi. xcv. figs. 3, 4; pi. xcvii. 
Alethopteris muricata, Roehl, Foss. Flora d. Steirik. Form. Westphalens, p. 78, pi. xi. fig. 1. 
Pseudopecopteris muricata, Lesqx., Coal Flora in Pennsyl., p. 203, pi. xxxvii. fig. 2. 
Filicites muricatus, Schlotheim, Flora d. Vorioelt, p. 54, pi. xii. figs. 21 and 23. 

Remarks.— Very rare. 
Locality : — Radstock. 



364 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

EXPLANATION OF PLATES. 

Plate XIX. 

Fig. 1. Sphenopteris Wpodwardi, Kidston, n. sp., Camerton (nat. size), p. 348. 

Fig. la.b.c. Sphenopteris Woodwardi, pinnules enlarged, showing nervation. 

Fig. 2. Sphenopteris tenuifolia, Gutbier (Brongt. ?), Upper Conygre Pit, Timsbury (nat. size), p. 345. 

Fig. 2a.b. Sphenopteris tenuifolia, pinnules enlarged 3 times, showing nervation. 

Fig. 3. Sphenopteris species, Old Mills Pit, Farrington, Guerney (nat. size). Farrington Series, p. 411. 

Plate XX. 

Fig. 1. Schizostach ys sphenopderoides, Kidston, n. sp., Radstock (nat. size), p. 352. 
Fig. la. Schizostachys sphenopderoides, sporangia enlarged 3 times. 
Fig. 2. Ptycliocarpus oblongus, Kidston, n. sp., Camerton (nat. size), p. 350. 
Fig. 2a. PtyclwcarpMs oblongus, two pinnules enlarged 3 times. 
Fig. 2b. Ptycliocarpus oblongus, synanguim? further enlarged. 

Fig. 3. RhaeophyUum spinosum, Lesquereux, Radstock (nat. size). Specimen in the collection of 
Mr J. M'Murtrie, p. 389. 

Plate XXI. 

Fig. 1. Sphenopteris gcniculata, Germar and Kaulfuss, Kilmersdon Pit (nat. size), p. 346. 

Fig. \a.b. Sphenopteris geniculata, pinnules enlarged, showing nervation. 

Fig. 2. Neuropderis macrophylla, Brongt., Braysdown (nat. size), p. 354. 

Fig. 3. Neuropderis fimbriata, Lesquereux, Wellsway Pit (nat. size), p. 361. 

Fig. 4. Neuropderis fimbriata, Camerton (nat. size). 

Fig. 5. Neuropteris fimbriata (1), Upper Conygre Pit, Timsbury (nat. size). 

Fig. 6. DictyopAeris M-iinsteri, Eichwald, sp., Camerton (nat. size), p. 361. 

Fig. 6a.b. Dictyopteris Mmisteri, pinnules enlarged, showing nervation. 

Plate XXH. 

Fig. 1 . Neuropteris ovata, Hoffmann, Camerton (nat. size), p. 359. 

Fig. la. Neuropteris ovata, pinnule enlarged 2\ times, to show the nervation. 

Fig. 2. Neuropteris macrophylla, Brongt., Radstock (nat. size), p. 354. 

Fig. 2a. Neuropteris macrophylla, pinnule enlarged 2 times, to show the nervation. 

Fig. 3. Neuropderis macrophylla, Radstock (nat. size). Specimen in the collection of the Bath 

Museum. 

Fig. 3a. Neuropderis macrophylla, portion of pinnule enlarged, to show the nervation. 

Plate XXIII. 

Fig. 1. Neuropteris Scheuchzeri, Hoffmann, Radstock (nat. size). Specimen in the collection of the 

Bath Museum, p. 356. 
Fig. la. Neuropderis ScJieuchzeri, portion of pinnule enlarged, to show the hairs. 
Fig. 2. Neuropderis Scheuchzeri, portion of pinnule enlarged 3 times, to show the nervation. 
Fig. 3. Trigonocarjms Nocggerafhi, Brongt. (nat. size). In the collection of Mr J. M'Murtrie, p. 403. 
Fig. 4. Rhabdocarpius multistriatus, Presl, sp., Radstock (nat. size), p. 404. 
Fig. 5. Cardiocarpus Outbiere, Geinitz, Radstock (nat. size). In the collection of Mr J. M'Murtrie, 

p. 403. 
Fig. 6. Cardiocarpus, Upper Conygre Pit, Timsbury (nat. size), p. 403. 
Fig. 7. Carpolithus ovoideus, Goppert and Berger, Wellsway Pit (nat. size), p. 404. 
Fig. 8. Carpolithus ovoideus, Camerton (nat. size). 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 365 



PAKT II. 

(Read 6th June 1887.) 

Pecopteris, Brongniart. 

Pecopteris, Brongt., Sur la Classification des Vegetaux Fossiles, p. 33, 1822. 
Cyatheites, Goppert, Sijst. fil. foss., p. 319, 1836. 
Asterocarpus, Goppert, Syst. fil. foss., p. 188, 1836. 
Scolecopteris, Zenker, Linncea, vol. xi. p. 509, 1837. 
Hawlea, Corda, Flora protogoea, p. 90, 1845. 

Remarks. — Several generic names, originating from some supposed likeness 
to recent genera, or from the arrangement of the sporangia, have been proposed 
by different authors for the ferns included here, and which were originally 
placed by Brongniart in his genus Pecopteris. 

The name Cyatheites was given by Goppert to certain members of the genus 
on account of their supposed resemblance to some of the Cyathea. This 
supposed resemblance was dependent in great measure on imperfect preserva- 
tion of the fruit. 

The genus Asterocarpus of the same author was founded to comprise certain 
Pecopterids, in which the exannulate sporangia are arranged in a stellate manner ; 
the greater number of his Cyatheites are now known, from the structure of their 
fruit, to belong to his Asterocarpus. 

In Scolecopteris, Zenker, the exannulate sporangia are also arranged in 
stellate groups, but the individual sporangia are produced upwards in a sharp 
point, thus differing from Asterocarpus, where the sporangia are short. 

Hawlea, Corda, is most probably identical with Asterocarpus. 

The upper surface of the pinnules of many species of Pecopteris is covered 
with short closely adpressed hairs. This villosity has been observed on many 
of the Radstock species, viz., — Pec. arborescens, Pec. arbor escens, var. cyathea, 
Pec. oreopteridia, Pec. villosa, and Pec. Milto?ii (Pec. abbreviata), and I have also 
observed the same character on specimens of typical Pec. Miltoni, from Clay- 
cross, Derbyshire, and Ashton-under-Lyne, Lancashire, and on Pec. polymorpha 
from the Forest of Dean. On several of these species a villosity has pre- 
viously been observed. It is probable that this villosity will be found to 
be much more common in the genus Pecopteris than generally supposed, 
as it is only observable on specimens in an exceptionally good state of 
preservation. 

The fruit of many of the species of the genus has been observed and 
described. 



366 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 



Pecopteris arborescens, Schlotheim, sp. 

Pecopteris arborescens, Brongt., Hist. d. veget. fuss., p. 310, pis. cii. ; ciii. ; figs. 2, 3. 

Pecopteris arborescens, Germar, Vers. v. Wettin u. Lobejun, p. 97, pis. xxxiv, xxxv. (fig. 4 1). 

Pecopteris arborescens, Grand' Eury, Flore Carbon du Depart, de la Loire, p. 68, pi. viii. fig. 6. 

Pecopteris arborescens, Zeiller, VegSt.foss. d. ten: houil., p. 81, pi. clxix. fig. 4. 

Pecopteris arborescens, Kidston, Catal. Pakeoz. Plants, pp. 113 and 253. 

Cyatheites arborescens, Geinitz, Vei's. d. Steinlif in Sachsen, p. 24, pi. xxviii. figs. 7-1 1 . 

Cyatheites arborescens, Heer, Flora foss. Helv., p. 27, pi. viii. figs. 1-4. 

Cyathocaipus arborescens. "Weiss, Foss. Flora d. jiingst. Stl: u. d. Rothl., p. 84. 

Filicites arborescens, Scblotheim, Flora d. Vorwelt, p. 41, pi. viii. figs. 13, 14. 

Pecopteris platyrachis, Brongt., Hist. d. veget. foss., p. 312, pi. cii. figs. 4, 5. 

Pecopteris aspidioides, Brongt., Hist. d. veget. foss., p. 311, pi. cxii. fig. 2. 

Asplenites nodosus, Gopp., Syst. fil. foss., p. 280, pi. xix. figs. 1-3. 

Pecopteris cyatheoides, Schintper, Traite d. paleont. veget., vol. i. p. 523, pi. xli. fig. 14. 

Pecopteris cyathea, Brongt., Hist. d. veget. foss., p. 307, pi. ci. figs. 1-3 (excl. fig. 4 = P. Candolliana). 

Pecopteris cyathea, Grand' Eury, Flore Carbon d. Depart, de la Loire, p. 68, pi. viii. fig. 7. 

Pecopteris cyathea, Zeiller, Veget. foss. du terr. houil., p. 82, pi. clxix. figs. 5, 6. 

Filicites cyatheus, Schlotheim, Flora d. Vorwelt, p. 38, pi. vii. fig. 11. 

Asjndites decussaius, Gopp., Syst. fil. foss., p. 369, pi. xxvi. figs. 1, 2. 

Remarks. — In typical Pec. arborescens the veins are simple ; in the form 
distinguished by Schlotheim as Filicites cyatheus the veins are sometimes 
simple, but usually once divided, and even occasionally divided three times. 
The pinnules are also more oblong than in typical Pec. arborescens. 

The majority of botanists unite Pec. cyathea with Pec. arborescens, but, 
among recent writers, Zeiller and Grand' Eury keep them separate. The 
species is very common in the Radstock area, and occurs in a very fine state 
of preservation. After carefully examining many examples, though the speci- 
mens can generally be referred to their respective forms without much difficulty, 
they are so connected by intermediate conditions that I can only regard Pec. 
nrhorescens and Pec. cyathea as different states of one species. 

The upper surface of the pinnules of some of the typical specimens of 
Pec. arborescens and the form cyathea is covered with short adpressed hairs, 
similar to those on the specimen of Pec. (Scolecopteris) cyathea figured by 
Stur."" 

The Asplenites nodosus, Gopp., is only a somewhat imperfectly preserved 
fruiting specimen of Pec. arborescens, and his Aspidites decussatus is apparently 
the corresponding condition of Schlotheim's Filicites cyatheus. Specimens 
agreeing with both these so-called species have been collected. 

The form cyathea is of as frequent occurrence as typical Pec. arborescens. 

Localities: — Radstock; Wellsway Pit, Braysdown; Kilmersdon Pit; Upper 
Conygre Pit ; Camerton. 

* Stur, Sitzb. d. I,: Akad. d. Wissensch., vol. Ixxxviii. Abth. i. p. 750, fig. 25, 1883. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 367 

Pecopteris Candolliana, Brongniart. 

Pecopteris Candolliana, Brongt., Hist, d. veget. foss., p. 305, pi. c. fig. 1. 

Pecopteris Candolliana, Germar, Vers. v. Wettin u. Lobejun, p. 108, pi. xxxviii. 

Pecopteris Candolliana, Grand' Eury, Flore Carb. du Depart, de la Loire, p. 69, pi. viii. fig. 8. 

Pecopteris Candollei, Zeiller, Veget. foss. du terr. houil., p. 84. 

Ctjathocarpus Candolleanus, Weiss, Foss. Flora d. jiingst. Stk. u. d. Rothl., p. 85. 

Pecopteris affinis, Brongt. (not Schlotheim), Hist. d. veget. foss., p. 306, pi. c. figs. 2, 3. 

Pecopteris cyatliea, Brongt. (in part), Hist. d. veget. foss., pi. ci. fig. 4. 

Remarks. — -Very rare. 

Localities : — Kadstock ; Braysdown Colliery. 

(f) Pecopteris asper, Brongniart. 

Pecopteris asper, Brongt., Hist. d. veget. foss., p. 339, pi. cxx. figs. 1-4. 

Pecopteris asper, Zeiller, Bidl. soc. geol. d. France, 3 e ser., vol. xii. p. 202 ; Flore foss. d. Bassin 
Houil. d. Valenciennes, pi. xxix. figs. 1-3. 

Remarks. — I refer to this species two small specimens collected at Timsbury, 
but, owing to their fragmentary nature, it is desirable that more perfect 
examples be examined before definitely recording the occurrence of this 
species. 

Locality : — Upper Conygre Pit. 

Pecopteris pennseformis, Brongniart. 

Pecopteris pennceformis, Brongt., Hist. d. veget. foss., p. 345, pi. cxviii. figs. 3, 4. 

Pecopteris pennaiformis, Brongt., Class, d. veget. foss., p. 33, pi. ii. fig. 3. 

Pecopteris pennceformis, Schimper, Traite d. paleont. veget., vol. i. p. 505. 

Pecopteris pennaiformis, Zeiller, Bull soc. geol. d. France, 3 e ser., vol. xii. p. 201, 1883 ; Flore foss. 

d. Bassin houil. d. Valenciennes, pi. xxx. figs. 1-4. 
Pecopteris cequalis, Brongt., Hist. d. veget. foss., p. 343, pi. cxviii. figs. 1, 2. 

Remarks. — Extremely rare, only a single specimen having been met with. 
Locality ; — Camerton. 

Pecopteris unita, Brongniart. 
PL XXIV. figs. 2-9. 

Pecopteris unita, Brongt., Hist. d. veget. foss., p. 342, pi. cxvi. figs. 1-5. 

Pecopteris unita, Kidston, Catal. Palwoz. Plants, p. 122 (excl. syn. Pecopteris elegans). 

Pecopteris unita, Grand' Enry, Flore Carb. du Depart, de la Loire, p. 76, pi. viii. fig. 13. 

Pecopteris unita, Lesqx., Coal Flora of Pennsyl., p. 223, pi. xl. figs. 1-7. 

Cyatheites unitus, Geinitz, Vers. d. Steinkf. in Sachsen, p. 25, pi. xxix. figs. 4, 5. 

Cyathocarpus unitus, Weiss, Foss. Flora d. jiingst. Stk. u. d. Rothl., p. 88, pi. xii. figs. 5, 6. 

Goniopteris elliptica, Font, and White, Perm, or Upper Carb. Flora, p. 83, pi. xxx. fig. 1. 

Pecopteris unita, forma emarginata, Gopp., sp. 

Pecopteris longifolia, Brongt., Hist. d. veget. foss., p. 273, pi. lxxxiii. fig. 2. 
Pecopteris longifolia, Germar, Vers. v. Wettin u. Lobejun, p. 34, pi. xiii. figs. 2-4. 
Stichopteris longifolia, Weiss, Foss. Flora d. jiingst. Stk. u. d. Rothl., p. 97, pis. ix., x. figs. 7, 8. 
Pecopteris emarginata, Bunbury, Quart. Jour. Geol. Soc, vol. ii. p. 86, pi. vi., 1846. 
Pecopteris emarginata, Lesqx., Coal Flora of Pennsyl., p. 225, pi. xxxix. fig. 11. 
Diplazites emarginatus, Gopp., Syst. fil. foss., p. 274, pi. xvi. figs. 1, 2. 
VOL. XXXIII. PART II. 3 I 



368 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Remarks. — This species is common throughout the whole of the Eadstock 
area, but usually occurs in a fragmentary condition, seldom more than isolated 
pinnae being met with. 

Many botanists regard Pec. emarginata, Gopp., sp. ( = Pec. longifolia, Brongt, 
not Sternb.), as specifically distinct from Pec. unita, Brongt. ; on the other hand, 
some regard them as only different portions of one species. 

I have carefully collected specimens of the plants that have been referred 
respectively to Pec. unita, Brongt,, and Pec. emarginata, Gopp., sp., and com- 
pared them with specimens of the latter species from Wettin, with which many 
of the Eadstock examples agree, but have failed to discover any character by 
which Pec. emarginata can be separated specifically from Pec. unita. They 
seem to me so to pass into each other that their separation appears arbitrary, 
and not determined by any fixed character peculiar to either form. 

A few specimens in fruit, identical with Weiss's figure of Stichopteris 
emarginata { — Pec. emarginata, Gopp., sp.), have also been met with. 

For the satisfaction of those who may regard Pec. emarginata as a distinct 
species, its distribution is given separately under the distinction of Pec. unita, 
forma emarginata. 

Description of Specimens Figured. 

PL XXIV. fig. 3, Pec. unita, Brongt. ; from New Mills Pit {Farrington Series). 
— This sketch shows the typical plant as figured by Brongniart in his Hist. d. 
veget. foss., pi. cxvi. fig. 1. On the lower pinnae the pinnules are separate to 
the base, but as the pinnae approach the apex of the specimen (which from the 
inequality of the pinnae on the two sides of the rachis is evidently a pinna and 
not the terminal portion of a frond), the pinnules become more or less united 
among themselves, till on the uppermost pinnae the pinnules are so completely 
united that the pinnae appear entire or only slightly dentate. At fig. Sa are 
given two pinnules, enlarged 2 times, from a lower pinnae, to show the nerva- 
tion. 

The veinlets are sometimes almost straight, but usually curved upwards 
(as in fig. i)a), though occasionally curved outwards (as in fig. da). 

PI. XXIV. fig. 9, Pec. unita, Brongt. ; Camerton. — This figure shows the 
pinnules united to each other for about two-thirds of their entire length. The 
specimen is a portion of a primary (?) pinna nearer its base than that just 
described (fig. 3), and corresponds to Brongniart's fig. 5, pi. cxvi. The veinlets 
are curved upwards, — the two contiguous basal veinlets coalescing and extend- 
ing to the base of the notch that separates the free portions of neighbouring 
pinnules. This arrangement of the nervation — the union of the two basal 
contiguous veins and the formation of a veinless triangle at the base and 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 369 

between the contiguous pinnules — has induced some botanists to employ 
Presl's genus Goniopteris for this and some allied species. 

PI. XXIV. fig. 5, Pec. unita, Brongt. ; Old Mills Pit (Farrington Series). — 
This small specimen differs from the last in the segments being slightly more 
elliptical, the specimen being in fact the Goniopteris elliptica, Fontaine and 
White.* 

PI. XXIV. fig. 4, Pec. unita, Brongt. ; Camerton. — This would perhaps be 
regarded by some as Pec. longifolia, Brongt., but I believe it to be the upper- 
most entire pinnse of Pec. unita. A like view is taken of a similar specimen 
figured by Weiss in his Foss. Flora d. jilngst. Stk. u. d. Rothl., pi. xii. fig. 5. 

Probably the Pec. lanceolata, Lesqx., should also be referred to Pec. unita as 
its upper portion. t 

PI. XXIV. fig. 6, Pec. unita, forma emarginata ; Camerton. — This specimen 
is clearly the Pec. longifolia, Brongt. ( — P. emarginata, Gopp.). J Enlarged draw- 
ings of the nervation are given at fig. 6a. In comparing this specimen with 
that given at fig. 4, the differences are not greater than what occur in pinnae 
situated on different parts of the same frond. 

Figs. 4 and 6 are similar to the specimens Germar has figured as Pec. longi- 
folia in his Vers. d. Steink. v. Wettin u. Lobejun, fasc. 3, pi. xiii. My fig. 4 
corresponds to his fig. 2, and my fig. 6 to his figs. 3, 4. 

PI. XXIV. figs. 7, 8, Pec. unita, forma emarginata. Fig. 7 from Eadstock ; 
fig. 8 from Upper Conygre Pit, Timsbury. — These figures also represent the 
Stichopteris longifolia, Brongt., sp., of Weiss,§ which is evidently similar to Pec. 
emarginatus, Gopp., sp., as figured by Bunbury. 

PI. XXIV. fig. 2, Pec. unita, forma emarginata; from Camerton. — This 
specimen would also be referred, by those who regard Pec. unita and Pec. 
emarginata or longifolia as distinct species, to the latter plant. 

In regard to the various figures I have given in illustration of the different 
forms assumed by Pec. unita, if only characteristic specimens of Pec. unita, 
Brongt. (fig. 3), are dealt with on the one hand, or those characteristic of 
Pec. longifolia (figs. 2 and 6) on the other hand, one would probably be led to 
conclude that there were here two very distinct species. When, however, a large 
series of specimens is examined, these two supposed species are so intimately 
connected by intermediate forms that I have found myself unable definitely to 
say where Pec. unita ends and Pec. emarginata begins. I therefore class the 
latter as a form of Pec. unita. 

* Perm, or Upper Carb. Flora, p. 83, pi. xxx. fig. 1. 

f Pecopteris lanceolata, Lesqx., Coal Flora of Pennsyl., p. 227, pi. xxxix. figs. 9, 10 = Alethopteris 
lanceolata, Lesqx., Geol. Rep. of Illin., vol. iv. p. 398, pi. xiii. figs. 1-3. 
\ Hist. d. veget. foss., pi. lxxxiii. fig. 2. 

§ Foss. Flora d. jilngst. Stk. u. d. Rotlil., pis. ix., x. figs. 7, 8. 
|| Quart. Jour. Geol. Soc, vol. ii. p. 86, pi. vi., 1846. 



370 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 



in error.* 



In my Catalogue of Palwozoic Plants I united Pec. elegans with Pec. unita 

error.* 

Localities : — 

Pec. unita, Brongt. 

Eadstock ; Braysdown Colliery ; Upper Conygre Pit ; Lower Conygre Pit ; 
Kilmersdon Pit ; Wellsway Pit ; Camerton. 

Pec. unita, Brongt., forma emarginata, Gopp., sp. 

Wellsway Pit ; Braysdown Colliery ; Camerton ; Radstock ; Upper Conygre 
Pit. 

Pecopteris villosa, Brongniart. 

Pecopteris villosa, Brongt., Hist. d. veget. foss., p. 316, pi. civ. fig. 3. 

Remarks. — This species is included here merely as having been founded by 
Brongniaet on a specimen from near Bath. 

It is now well known that the outer surface of the pinnules of various 
species of Pecopteris possesses a villosity, and as this villosity often quite obscures 
the veins, it is occasionally extremely difficult, if not even impossible, to 
determine to which species such specimens should be referred. Zeiller 
suggests that Pec. villosa may perhaps belong to Pec. abbremata, Brongt. 
( — Pec. Miltoni, Artis), but as the nervation on the type specimen is obliterated, 
it is quite impossible, in the absence of this most important character for 
the specific determination of the members of the genus Pecopteris, to decide 
to which species it should be referred. 

Having observed a villosity on an undoubted specimen of Pec. oreopteridia, 
Schl., sp.,t and from the general outline of Pec. villosa, Brongt. agreeing so 
closely with that of Pec. oreopteridia, I am inclined to refer Pec. villosa to 
that species. The point, however, cannot be definitely settled from the meagre 
evidence before us.j 

Only one thing seems clear, that Pec. villosa, Brongt., most probably 
represents a condition of a species known under another name when the veins 
are not obscured by the villosity, and is not itself a plant possessing a true 
individuality. 

The Cijatheites villosus, Geinitz,§ is referable to Pec. abbremata, Brongt. 
( = Pec. Miltoni, Artis). 

Locality : — Near Bath {Brongniart). 

* Sec Zkillkh, Vri/f'f. foss. (I. terr. houil., p. 93, pi. clxvi. figs. 5, 6. 

t See PL XXVII. figs. 3, 4. 

X See Zeiller, "Notes sur la flore houillere des Asturies," Mem. Soc. Gcol. du Nord, 1882, p. 12. 

§ Vers. d. Steinkf. in Sachsen, pi. xxix. figs. 6-8. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 371 

Pecopteris oreopteridia, Schlotheim, sp. 
PL XXVII. figs. 3, 4; PL XXVIII. figs. 1, 2. 

Pecopteris oreopteridia, Brongt., Hist. d. veget. foss., p. 317, pi. civ. figs. 1, 2; pi. v. figs. 1, 2, 3. 
Pecopteris oreopteridia, Renault, Cours d. botan. foss., 1883, p. 110, pi. xviii. figs. 5, obis ; pi. xix. 

figs. 7-12. 
Pecopteris oreopteridia, Weiss, Foss. Flora d. jiingst. Stic. u. d. Rotlil., p. 66. 

Pecopteris oreopteridia, Zeiller, Bull. soc. geol. d. France, 3 e s£r., vol. xiii. p. 138, pi. ix. figs. 1, la. 
Cyatheites oreopteroides, Geinitz, Vers. d. Steirikf.in Sachsen, p. 25, pi. xxviii. fig. 14. 
Filicites oreopteridius, Schlotheim, Flora d. Vorwelt, p. 36, pi. vi. fig. 9. 

Remarks. — This species is common in the Radstock Series, and some very 
fine specimens have been collected. Of these, one which I received from Mr 
Job Moon, Camerton, deserves special note. This example shows three 
primary (?) pinnae springing from a common rachis, of which only the central 
primary pinna is perfect. It measures 14^ inches in length, and its greatest 
diameter, which is towards the centre of the pinna, is 6 inches. The pinna to 
the right of this one is longer, but, not being perfect, I am unable to give its 
exact measurements. In outline the primary pinnae are broadly lanceolate. 

Of the three primary (?) pinnae shown on the portion of the frond that 
has been preserved, the uppermost primary (?) pinna exhibits still, on the 
inferior side of its rachis, portions of 17 secondary (?) pinnae. These are all 
barren. 

The central primary (?) pinna bears about 36 pairs of alternate lanceolate 
secondary (?) pinnae, of which the 6 or 7 lower pairs are barren, or only bear a 
few fruiting pinnules ; the succeeding 6 or 7 pairs of pinnae are soriferous, the 
fruit being borne on the central pinnules of the pinnae. The remaining upper 
pinnae are barren. 

On the remaining and lowest of the three primary (?) pinnae preserved on 
the specimen, the 15 lowest secondary (?) pinnae are soriferous, the remaining 
upper pinnae being barren. 

Two secondary (?) pinnae from the central primary (?) pinna are shown on PL 
XXVIII. figs. 1, 2. On fig. 1 the fruiting pinnules are seen to occupy the central 
part of the pinna; on fig. 2 only the third pair from the base are soriferous. 

The most interesting point in connection with these soriferous pinnules is 
the occurrence on them of a dense villous covering. An enlarged drawing of 
such a pinnule is shown on PL XXVII. fig. 4. On a few of the barren pinnules 
a villosity can also be detected, but it is so slight that it cannot be compared in 
importance or prominence with that of the soriferous pinnules. 

An enlarged barren pinnule (PL XXVII. fig. 3) shows from its nervation 
that this specimen is clearly referable to Pec. oreopteridia, SchL, sp. 

Since detecting the presence of a villosity on the pinnules of Pec. oreopteridia, 



372 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

I have been led to suspect that perhaps Pec. villosa, Brongt., should be referred 
to this species. 

Localities : — Radstock; Braysdown Colliery; Upper Conygre Pit; Camerton. 



Pecopteris Cistii, Brongniart. 

Pecopiteris Cistii, Brongt., Hist. d. veget. foss., p. 330, pi. cvi. 

Remarks. — I only know this species from Brongniart's figures and descrip- 
tion. Of the two specimens figured by him, one came from Dunkerton, near 
Bath, and the other from Wilkesbarre, Pennsylvania. 

Dunkerton Pit is now closed, but I have carefully examined other localities 
where the same coals are worked in the hope of rediscovering this species, 
but have -hitherto been unsuccessful. Lesquereux says in regard to Pec. Cistii 
— " Though I have seen many fragments referred to it, I have never been able 
to positively recognise in any the characters indicated by the author."* I can 
fully endorse this statement, for, though I have also seen specimens labelled 
" Pec. Cistii" none of them possessed characters entirely in agreement with 
Brongniart's description, and were, 1 am afraid, only Pec. oreopteridia. 

The type from Dunkerton, which belonged to the Museum of the University 
of Oxford, appears to have been lost or mislaid, for, when visiting that collection 
a short time ago, we were unable to discover it. 

Locality : — Dunkerton (Br'ongniart). 

Pecopteris Bucklandii, Brongniart. 

Pecopteris Bucklandii, Brongt., Hist. d. veget. foss., p. 319, pi. xcix. fig. 2. 

Pecopteris Bucklandii, Grand' Eury, Flore Carb. du Depart, de la Loire, p. 75. 

Pecopteris Buclclandii, Scliimper, Traite d. paleont. veget, vol. i. p. 504. 

Pecopteris Bucklandii, Weiss, Foss. Flora d. jiingst. Stk. u. d. Rothl., p. 64. 

Pecopteris pseudo-Bucklandii, Germar, Vers. d. Steink. v. Wettin u. Lbbejun, p. 106, pi. xxxvii. 

Remarks. — This species is very rare, but a few examples have been collected 
at Camerton — the original locality. 

It is very doubtful if the fern figured as Pec. Bucklandii by Lindley and 
HuTTONt really belongs to this species. If their figure is correct, I am 
inclined to think that it does not. Stur suggests that Lindley and Hutton's 
plant may perhaps be his Hawlea Schaumberg-Lipjwana, but this is also very 
doubtful.^: 

Locality : — Camerton. 

* Coal Flora of Pennsyl., p. 244. 
f Fossil Flora, vol. iii. pi. ccxxiii. 
X Carbon-Flora d. Schatzlarer-Schichten, p. 120, pi. lvii. fig. 1 ; pi. lviii. figs. 1-4. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 373 



Pecopteris pteroides, Brongniart. 

Pecopteris pteroides, Brongt., Hist, d. veget. foss., p. 329, pi. xcix, fig. 1. 
Pecopteris pteroides, Germar, Vers. d. Steink. v. Wettin u. Lobejun, p. 103, pi. xxxiv. 
Pecopteris pteroides, Grand' Eury, Flore Carb. du Depart, de la Loire, p. 75. 
Asterocarpus pteroides, Weiss, Foss. Flora d.jiingst. Stk. u. d. RotKl., p. 91. 

Remarks. — Pec. pteroides is extremely rare ; the only specimen I have seen 
from the Radstock Series is one in the British Museum, labelled as coming 
from "near Bath." 

The figures given by Geinitz as Pec. (Alethopteris) pteroides do not appear 
to belong to this species.* 

Locality: — " Near Bath." 



Pecopteris crenulata, Brongniart. 

Pecopteris crenulata, Brongt., Hist., d. veget. foss., p. 300, pi. lxxxvii. fig. 1. 

Pecopteris crenulata, Zeiller, Bull. soc. geol. d. France, 3 e ser., vol. xii. p. 200, 1883 ; Flore foss. 
du Bassin houil. de Valenciennes, pi. xxv. figs. 1-4. 

Remarks. — I refer to this species a single specimen collected at Camerton. 
It is, however, possible that some other examples which I have not yet been 
able satisfactorily to identify may belong to this species. 

Locality : — Camerton. 



Pecopteris polymorpha, Brongniart. 

Pecopteris polymorplia, Brongt., Hist. d. veget. foss., p. 331, pi. cxiii. 

Pecopteris polymorpha, Grand' Eury, Flore Carb. du Depart, de la Loire, p. 74, pi. viii. figs. 10, 11. 

Pecopteris polymorpha, Renault, Cours d. botan. foss., p. 116, pi. xx. figs. 1-10, 1883. 

Pecopteris polymorpha, Zeiller, Veget. foss. d. terr. houil., p. 91, pi. clxix. figs. 1, 2, 3. 

Pecopteris Miltoni, Brongt. (not Artis), in part, Hist. d. veget. foss., pi. cxiv. figs. 2, 7 (other figs.?). 

Remarks. — Not common. A good fruiting example was collected at 
Radstock. 

I have detected the presence of short adpressed hairs on the upper surface 
of the pinnules of a specimen of this species from Trafalgar Colliery, near 
Drybrook, Forest of Dean. This villosity is so copious that on some of the 
pinnules the nervation is almost completely obscured. 

Localities : — Radstock ; Braysdown Colliery ; Camerton. 

* Vers, de Steinkf. in Sachsen, pi. xxxii. figs. 1-5. 



374 MR ROBERT KIDSTON" ON THE FOSSIL FLORA OF THE 



Pecopteris Miltoni, Artis, sp. 

Pecopteris Miltoni, Gerinar, Vers. d. Steinl: v. Wettin u. Lubejun, p. 63, pi. xxvii. (excl. syn. Pec. 

polymorpha, and P. Miltoni, Brongt., not Artis). 
Pecopteris Miltoni, Sterzel, Die Flora d. Ruthl. im nordwesi. Saclisen, p. 6, pi. i. (xxi.) figs. 1-7 

(in Dames & Kayser's Paleont. Abhandl., Band iii. Heft ii. p. 240 (excl. syn. Pec. 

polymorphs). 
Cyatheites Miltoni, Geinitz, Vers. d. Steinkf. in Saclisen, p. 27, pi. xxx. fig. 5 (fig. 6 '!), var. 

abbreviata, pL xxx. figs. 7-8 ; pi. xxxi. figs. 1 (2, 3 1), 4 (refs. in part). 
Filiates Miltoni, Artis, Antedil. Phytol., pi. xiv. 
Pecopteris crenata, Sternberg, Vers., i. p. xx. pi. x. fig. 7 ; ii. p. 154. 
Hawlea pulcherrima, Corda, Flora protogcea, p. 90, pi. lvii. figs. 7, 8. 

Hawlea Miltoni, Stur, Carbon-Flora, p. 108, pi. lix. and pi. lx. (excl. figs. 3-4., syn. in part). 
(?) Goniopteris brevifolia, Schimper, Traite d. paleont. veget., vol. i. p. 546. 
■Pecopteris abbreviata, Brongt., Hist. d. veget. foss., p. 337, pi. cxv. figs. 1-4. 
Pecopt&ris abbreviata, L. & H., Fossil Flora, pi. clxxxiv. 
Pecopteris abbreviata, Zeiller, "Notes sur la flore houillere des Asturies," p. 12, [Mem. Geol. Soc. du 

Nord, 1882) ; Flore foss. du Bassin houill. de Valenciennes, pi. xxiv. figs. 1-4, 1886. 
Cyatheites villosus, Geinitz, Vers. d. Steinkf. in Saclisen, p. 25, pi. xxix. figs. 6-8.* 

Remarks. — A great difference of opinion exists among botanists in regard 
to the specific value of Pec. Miltoni, Artis, sp., Pec. abbreviata, Brongt., and 
Pec. polymorpha, Brongt. 

For a few years I have carefully collected those species and visited several 
of the British Coal Fields where they occur, with the special object of satis- 
fying myself as to the true relations of Pec. Miltoni, Pec. abbreviata, and 
Pec. polymorpha to each other. 

Several authors have united them under one name.t In the barren 
condition, the discrimination of the species is often difficult. In Pec. poly- 
morpha the nervation is closer, the divisions of the veinlets more numerous 
and straighter than in Pec. Miltoni and Pec. abbreviata, where the nervation 
has often a slight flexuosity. Pec. abbreviata, as will be seen, I regard as 
identical with Pec. Miltoni. 

Even in the barren condition, I believe, Pec. polymorpha can be safely 
separated from all other species, if the specimens are well preserved and at 
all typical. Its fruit, however, at once establishes its individuality, and clearly 
separates it from Pec. Miltoni. 

Pec. Miltoni was described by Artis from El-se-car Colliery, near Milton 
Furnace, Yorkshire, in 1825 : — Pec. abbreviata by Brongniart from mines near 

* I am very doubtful if the following species referred by Stur to Pec. Miltoni should be so in- 
cluded : — Asplenites heteropliyllus, Gb'pp.; Aspl. crispus, Gopp. ; Baluntites Martii, Gopp. The follow- 
ing, also included by the same author, appear to me to have no connection with Pec. Miltoni: — 
Adiantites giganleus, Gopp. ; Cyclopteris ooliqua, L. & H. ; Schizopteris lactuca, ltoehl. (Foss. Flora 
Westph., pi. xviii.) ; and Cyclop, oblata, L. & Ii. 

t Geinitz, loc. cit.; Germar, loc. cit.; Sterzel, loc. cit. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 375 

Bath (Radstock Coal Field), and from the mines of Anzin, near Valenciennes, 
Department du Nord. 

I may mention here that the plants figured by Brongniart as Pec. Miltoni, 
Hist, d. veget.foss., pi. cxiv., with perhaps the exception of his fig. 8, probably 
do not belong to this species, but to his own Pec. polymorpha* Brongniart's 
figs. 2 and 7 evidently belong to Pec. polymorpha ; his figs. 1, 3, 4, 5, and 6 
most probably also belong to the same fern, but on these figures I express no 
definite opinion. His fig. 8 lias been raised to specific rank by Schimper, under 
the name of Goniopteris brevifolia, 3 ^ but I think it is referable to Pec. Miltoni. 
I have collected at Radstock specimens which I cannot distinguish from it. 
Brongniart's figure does not give much data from which to form any satis- 
factory opinion. 

The type of Pec. Miltoni has disappeared, but while visiting some museums 
and private collections in Lancashire, Yorkshire, and Derbyshire, where coals 
are worked on or about the same horizon as those from which Pec. Miltoni 
was derived, I met with a number of undoubted specimens of it ; but I am 
specially indebted to Mr George Wild, Bardsley Colliery, Ashton-under- 
Lyne, and to Dr Pegler, Stonebroom, Derbyshire, for facilities for examining 
specimens of this species. 

In my several visits to Radstock I also collected many fine specimens of 
the plant described as Pec. abbreviata by Brongniart. These specimens I have 
compared with the figures and descriptions of Pec. Miltoni and Pec. abbreviate/, 
and have also compared the specimens from different localities with each 
other, as well as with some from the Coal Field of Valenciennes, kindly sent 
me by M. Zeiller, but have failed to discover any character by which they 
can be separated. 

It is admitted by all, including those who regard Pec. Miltoni and Pec. 
abbreviata as distinct species, that Pec. abbreviata at all events is very poly- 
morphic, and those who are most intimate with this fern are most cognizant of 
this fact. 

Zeiller has carefully entered into this subject in his Notes sur la Jlore 
houillere des Asluries in his remarks on Pec. abbreviata. He describes the little 
hairs on the upper surface of the pinnules of this species, whose presence, 
often entirely obscuring the nervation, has led to its being identified as Pec. 
villosa, and as an instance he cites the identification of Pec. abbreviata as Pec. 
villosa by Geinitz.J 

Whether the Pec. villosa, Brongt., can be referred to Pec. abbreviata or not, 
must in the meantime from want of evidence remain an open question. 

* See Zeiller, Mem. Soc. Geol. du Nord, loc. cit. 
f Traite d. paleont. veget., vol. i. p. 546. 

% That this so-called Pec.' villosa is in reality the Pec. Miltoni ( = Pec. abbreoiata, Brongt.) will, I 
think, be admitted by all who have studied the subject. 

VOL. XXXITI. PART II. 3 K 



376 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

Referring to the specific value of Pec. Miltoni, Artis, sp., and Pec. abbreviata, 
Brongt., Zeiller says : — " In regard to the question whether Pec. Miltoni and 
Pec. abbreviata are not identical, and of which Pec. Miltoni is the older name, 
having been founded in 1825, though not arriving at a wholly sure conclusion, 
I incline meanwhile towards the negative. 

" The general form of the pinnules indicated by Artis appears very analogous 
to those of Pec. abbreviata, but the nervation is not figured, which renders a 
comparison almost impossible, this character being almost the only one by 
which one is able satisfactorily to support it ; further, the figure and diagnoses 
given by the author indicate the sori to be marginal, or almost marginal, while 
I have already mentioned that the groups of capsules of Pec. abbreviata cover 
all the inferior surface of the pinnule, and are by no means marginal. The 
figures given by Geinitz, under the name of Cyatheites Miltoni,* show likewise 
the fructification almost marginal (pi. xxx. figs. 6, 6a, and also Cyatheites Miltoni 
var. abbreviates, figs. 8, 8a, and 8b). This character of the disposition of the 
sori appears to me sufficiently important to compel one to regard Pec. abbreviata 
as decidedly distinct from Pec. Miltoni. When, as to its union with Pec. poly- 
morpha, proposed by various authors, it is hardly necessary to mention that the 
characters of the fructification separate absolutely these two species, Pec. 
abbreviata having the short capsules of Asterotheca, and Pec. polymorpha the 
long sharp capsules of Scolecopteris. They belong further to different horizons" 
(" niveaux differents ").t 

I must first refer to Pec. Miltoni as being of older date than Pec. abbreviata. 
As is frequently the case with Pec. abbreviata, in Pec. Miltoni the nerva- 
tion is seldom shown on account of the dense villosity with which the upper 

surface of the pinnules is covered. This 

villosity is in all respects identical to that 

occurring on the pinnules of specimens which 

have been distinguished as Pec. abbreviata, 

'•$£: & Brongt., from the Radstock Series. At text 

''Mm^m (^Pvrw ^& - ^ * s S* ven an enlarged drawing of three 

^B«fi. v -^J-d pTN - . pinnules of Pec. Miltoni, Artis, sp., from 

Pecopteris Mnioni, Artis, s P . Claycross, to show the nervation. This is 

Fi' 2. From Bardsley Colliery, Ashton-under- , . , . , ... „ . ./, ., 

Lyne, Lancashire. absolutely identical in all respects with the 

Figs. 3, 4. From Claycross, Derbyshire (Middle en l ar cr emen t f PeC. abbretiata, given by 

Coal Measures). & ' ° J 

Figures enlarged two diameters. BltONGNIART On llis pi. CXV. fig. 3«. There 

can be no doubt that the plant occurring at Claycross, Derbyshire (Middle 
Coal Measures), is the true Pec. Miltoni, as its growth, segmentation, and the 

* Vers. d. Steinkf. in Sachsen, p. 27, pi. xxx. figs. 5-8; pi. xxxi. figs. 1-4. 

t Zeiller, Notes sur la florc howllere ties Asturies, p. 13. I may remark in passing, that in 
England Pec. polymorpha and Pec. Miltoni (including Pec. abbreviata) occur on tho same horizon. 




RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 377 

general character of many of the specimens is identical with the figure given 
by Artis. 

Pec. Miltoni, Artis, sp. (whatever view may be taken of the relationship of 
Pec. abbreviata to it), is very polymorphic in the form and size of the pinnules. 
Artis has only figured one condition of his plant, a condition which probably 
corresponds to Brongniart's Pec. abbreviata, fig. 1. 

Brongniart gave several figures of his species, and these have been well 
supplemented by Zeiller. # Forms corresponding to the figures of these 
authors occur among the Yorkshire, Lancashire, and Derbyshire specimens of 
Pec. Miltoni; in the barren condition, neither from the form of the pinnules 
nor their nervation can I discover any fixed character by which Pec. abbreviata, 
Brongt., can be separated from Pec. Miltoni, Artis, sp. 

The only remaining point of comparison is the fructification. On this 
Artis says : — " Fructifications surrounding the leaflets near, but not entirely on 
ike margin." And again — " The fructifications seated on the back of the leaves 
are not so closely seated on the margin as is expressed in the plate." 

Many of the specimens of Pec. Miltoni which T have examined, from the 
counties already mentioned, are in fruit, though none have been in a condition 
to exhibit its minute structure, such as the number of sporangia that compose 
the sori, or the shape of the individual sporangia. These specimens, however, 
clearly indicate the position of the sori, which appear as little circular dots, as 
shown in the woodcut, figs. 2 and 3. 

Fig. 2 is a pinnse from a Lancashire example ; fig. 3 from a Derbyshire 
plant. On both, the position of the fruit, as clearly indicated, is not marginal. 
In fact Artis, in referring to his own figure, clearly states that the fruit is not 
so closely seated on the margin as is expressed on his plate. Now, if his 
figure be carefully examined, it will be seen that on many of the pinnules the 
fruit holds almost a central position between the margin and the midrib, and 
certainly if it is not so near the margin as represented, it cannot be other than 
situated almost midway between the midrib and the margin, and then the sori 
will cover the whole of the under surface of the pinnule, as figured by ZEiLLER.t 
In the pinnae, where the pinnules are united throughout the greater part of 
their length, the fruit forms a single or double row along the midrib of the 
pinnas ; or, in other words, the pinnules only bear one or two groups of sori, 
situated at their base, as seen in woodcut, fig. 2. 

Fig. 3 shows two pinnules densely clothed on their upper surface with short 
hairs,| which quite obliterate the veins. The fruit is seen as circular dots 
holding a similar position to those figured on Pec. abbreviata by Zeiller. From 

* Flore foss. du Bassin liouil. d. Valenciennes, pi. xxiv. 

t Loc. cit, pi. xxiv. figs. 3, 4, 4a, 4b. 

X These are also present on most of the pinnae of the specimen from which fig. 1 was taken. 



378 MR ROBERT K1DST0N ON THE FOSSIL FLORA OF THE 

the examination of several such specimens I am led to conclude that the fruit 
of Pec. Miltoni, Artis, sp., and Pec. abbreviata, Brongt., is essentially the same, 
and therefore there exists no specific difference between Pec. Miltoni and Pec. 
abbreviate!, hence Brongniart's species must be united with Pec. Miltoni, 
Artis, sp. 

Remarks on some Figures of the Species. 
Pec. Miltoni, Gerinar, Vers. v. Wettin u. Lobejun, Heft 6, pi. xxvii. 1849. 

The figures given here are very characteristic of Pec. Miltoni, Artis, sp. 
The nervation agrees entirely with that of the specimens from Lancashire, 
Yorkshire, and Derbyshire. His fig. 2 corresponds to Artis's type. 

I have received from Dr Weiss a specimen of Pec. Miltoni from Wettin, 
which confirms this opinion. 

Geinitz, Vers. d. Steinkf. in Sachsen, 1855. 

Cyatheites Miltoni, pi. xxx. figs. 5, 6 ; pi. xxxi. figs. 1-4. 
Cyatheites Miltoni, var. abbreviatus, pi. xxx. figs. 7, 8. 

Of these, fig. 5 (pi. xxx.) is characteristic of Artis's species, but I have never 
seen the fruit as represented at fig. 6. Fig. 8 (pi. xxx.) probably corresponds 
to my woodcut, fig. 2. PL xxxi. fig. 4, gives a fair idea of the position of the 
fruit. Fig. 3 probably does not belong to Pec. Miltoni ; it is not, at all events, 
a characteristic figure of the species. 

It must be noticed that in all the fruiting examples given by Geinitz the 
sori are immature, and only represented by circular swellings. Were the sori 
more fully developed, they would occupy a much larger area of the surface of 
the pinnule. 

Ilawlea Miltoni, Stur, Carbon-Flora, pi. xlix. fig. 1, 1885. 

Though no enlarged details of this specimen are given, the fossil as repre- 
sented in the plate is absolutely identical with typical Pec. Miltoni. All the 
other figures in this plate are too indistinct to admit of any criticism. PI. xl. 
figs. 3, 4, I exclude from Pec. Miltoni. 

Pec. Miltoni, Sterzel, Flora d. llothliegenden im nordiv. Sachsen, pi. i. figs. 1-7.* 

The figures given here, though small, possess the characters of Pec. 
Miltoni. 

* In Dames and Kayser, Palceontolor/ische Abliandl., vol. iii. Heft. 4, p. 237, Berlin, 1886. 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 379 

Haivlea pulcherrima, Corda, Flora protogaza, pi. lvii. figs. 7, 8, 1845. 

I have already stated my belief that H. pulcherrima is a fruiting specimen 
of Pec. Miltoni, Artis, sp.* Stub, gives as the difference between the fruit of 
H. pulcherrima and Pec. Miltoni, that the former has shorter and broader 
pinnules {Tertiardbschnitte) and shorter and broader sporangia than Pec. 
Miltoni, where the pinnules and sporangia are narrower and longer. The fern 
being so polymorphic, and the form of the pinnules so greatly depending on 
their position on the frond, render this difference in form as a specific character 
in the case under discussion quite valueless. In regard to the other supposed 




Fig. 5. (Nat. size.) 

Fee. Miltoni, Artis, sp. { = H. pulcherrima, Corda), Forest of Wyre, Worcestershire. 

In the collection of the British Museum.t 

distinguishing character — the form of the sporangia, — the slight differences 
pointed out by Stue are far too slight to be of real value : they are even scarcely 
distinguishable in his text figure which illustrates this point, j and entirely 
disappear when H. pulc/wrrima is compared with Zeiller's figures of the fruit 
of Pec. (abbreviata) Miltoni.^ 

I give a text figure (5) of a specimen from the Forest of Wyre, Worcester- 
shire, in the collection of the British Museum, which appears to me to be at 

* Catalogue of Palceoz. Plants, p. 121. In the remarks here appended to Pec. Miltoni I have 
inadvertently referred to H. pulcherrima as Hawlea " elegans." I have also (p. 256) referred A. 
aquilina, Geinitz, Vers. d. Steinhf. in Sadism, pi. xxxi. figs. 5-7, to Pec. Miltoni. I still think it pro- 
bable that his figures 6, 7 are referable to this species, but am more doubtful about his figure 5. They 
are therefore omitted meantime from the synonymy of Pec. Miltoni, Artis, sp. 

t I am indebted to Dr Woodwart, F.R.S., for permission to describe this specimen. 

i Loc. cit, p. 106, fig. 17. § Loc. cit., pi. xxiv. tigs. 3, 4. 



380 MR ROBERT KIDSTON ON THE FOSSIL FLORA OF THE 

once the H. pulckerrima of Corda and the fruit of Pec. Miltoni. The fossil 
occurs as a dark brown impression of the lower surface of the frond on a 
yellow-brown matrix. On the left of the rachis, of which only a small portion 
is shown, are the remains of 7 pinnae. The 3 lower ones are imperfect, but the 
4 upper show their complete length. The pinnules at the base of the pinnae 
are contiguous and oblong, with blunt apices; the upper pinnules are confluent. 
The whole of the surface of the pinnules is thickly covered with stellate groups 
of sporangia, hence the veins are only seen at a few points of the specimen, and 
even then indistinctly. The sporangia are oval, and arranged in stellate groups 
of 3-6 sporangia, though 4 is the common number in each little star. The 
central point of attachment of the groups of sporangia is situated midway 
between the central vein and the margin of the pinnule, which latter bears a 
greater or less number of sori. In this example the pinnules near the apex of 
the pinnae bear very few sori ; those about the centre bear three on each side of 
the midrib, whilst the lowest pinnules bear 5 or 6 sori on each side of the main 
nerve. The little stellate groups of sporangia measure in their greatest dia- 
meter 1 mm. to 15 mm., the individual sporangia ranging from *5 to 75 mm. 
This specimen was associated with barren examples of Pecopteris Miltoni, 
Artis, sp. 

Localities: — Radstock ; Braysdown Colliery; Camerton ; Welton ; Wells - 
way Pit ; Lower Conygre Pit, 

Pecopteris Lamuriana, Heer. 

Pecopteris Lamuriana, Heer, Urwelt der Schweiz, p. 13, fig. 12. 

Pecopteris Lamuriana, Zeiller, Bull. soc. geol. d. France, 3 e ser., voL xiii. p. 139. 

Alethopteris Lamuriana, Heer, Flora foss. Helv., p. 32, pi. xii. figs. 6, 7. 

Remarks. — This species is very rare, only two specimens having been 
collected. 

Localities : — Radstock ; Braysdown Colliery. 

Pecopteris pinnatifida, Gutbier, sp. 

Neuropteris pinnatifida, Gutbier, Vers. d. Zwiclc. SchwarzJcohl, p. 61, pi. viii. figs. 1-3. 
Neuropteris pinnatifida, Gutbier, Vers. d. Zechst. u. Rothl., p. 13, pi. v. figs. 1-4. 
Pecopteris pinnatifida, Scbimper, Traite d. paleont. veget, vol. i. p. 507. 

Pecopteris Geinitzii, Gutbier, Vers. d. Zechst. u. Rothl., p. 16, pi. ii. fig. 10; pi. ix. figs. 1-3; 
pi. xi. figs. 5, 6. 
1 Pecopteris fruticosa, Gutbier, Vers. d. Zechst. u. Rothl., p. 16, pi. v. figs. 8. 9. 
Asterocarpus pinnatifidus, Weiss, Foss. Flora d.jungst. 8th, u. d. Rothl., p. 93. 

Remarks. — Of this fern four specimens have been collected, — three at 
Radstock and one at the Upper Conygre Pit, Timsbury. The figures given by 
Gutbier of this species are very rough, but with the plant as figured in his 



RADSTOCK SERIES OF THE SOMERSET AND BRISTOL COAL FIELD. 381 

Vers. d. Zwick. Schivarzkohl, pi. viii. figs. 1-3, and in his Vers. d. Zechst. u. 
Rothl., pi. v. figs. 1, 2, the Somerset examples agree entirely. 

The nervation of this species is described by Gutbier as " nerves strong, 
once bifurcated, in pairs, or fascicled (fiderig) according to the pinnulation."* 

In the almost entire pinnules of one of our specimens, one of the arms of 
the dichotomously divided lateral veins usually divides again. 

Pec. Geinitzii has been united with Pee. pinnatijida by Weiss and Schimper, 
and in this I have followed them. Such a course, however, makes it difficult 
to reconcile the two figures given by Gutbier of the fruit of his Pec. pinnatijida t 
with those he gives of the fruit of his Pec. Geinitzii, which is Asterocarpous ! 

Localities : — Radstock ; Upper Conygre Pit. 

Corynepteris, Baily. 

Corynepteris, Baily, Geol. Survey of Ireland, Explan. to accompany Sheet 142, p. 16, I860. 
Grand' Eurya, Zeiller, Ann. d. sc. not. Bot., 6 e s^r., vol. xvi. p. 203, 1883. 

Corynepteris erosa, Gutbier, sp. 

Pecopteris erosa, Gutbier, Gaea von Sachsen, p. 81. 

Pecopteris erosa, Lesqx., Coal Flora of Pennsyl., vol. i. p. 255, pi. xliv. figs. 1 and 3-. 
Alethopteris erosa, Geinitz, Vers. d. Steinkf. in. Sachsen, p. 29, pi. xxxii. figs. 7-9. 
Grand' Eurya erosa, Zeiller, Ann. d. sc. nat. Bot., vol. xvii, p. 9, 1884. 

Remarks. — Very rare. Only one specimen of this species has come under 
my notice from the Radstock Series. 

From the structure of the fruit of this fern, Zeiller places it in his genus 
Grand' Eurya, but from an examination of the type of Corynepteris, Baily, I 
am led to conclude that Zeiller's Grand' Eurya is identical with Baily's 
Corynepteris, and the latter, being the older generic name, is here adopted. 

Locality : — Camerton. 



Dactylotheca, Zeiller, Ann. d. sc. nat. Bot., 6 e ser., vol. xvi. p. 184, 1883. 
Dactylotheca plumosa, Artis, sp. 

Filicites plumosa, Artis, Antedil. Phyt., p. 17, pi. xvii. 

Pecopteris plumosa, Brongt, Hist, de veget. foss., p. 348, pis. cxxi. cxxii. 

Pecopteris delicatula, Brongt., Hist. d. veget. foss., p. 349, pi. cxvi. fig. 6. 

Aspidites Silesiacus, Gopp., Syst. fit. foss., p. 346, pis. xxvii. and xxxix. fig. 1. 

Senftenbergia crenata, Stur (not L. & H.) (in part), Carbon-Flora, p. 72, pi. xlv. fig. 1 (?). 

Senftenbergia plumosa, Stur (in part), Carbon-Flora, p. 91, pi. li. fig. 1 (figs, indistinct, excl. 

syn. Pec. pennceformis, Brongt.). 
Dactylotheca plumosa, Kidston, Catal. Palwoz. Plants, p. 128 (excl. syn. Pec. acuta). 
Pecopteris dentata, L. & H., Fossil Flora, vol. ii. pi. cliv. 

* Vers. d. Zwick. Schicarzkohl, p. 61. 

f Vers. d. Zechst. u. Rothl., pi. v. figs. 3, 4. 



382 ME ROBERT KIPSTON ON THE FOSSIL FLORA OF THE 

Dactylotheca plumosa, var. dentata, Brongt., sp. 

Pecoptens dentata, Brongt., Hist. d. veget. foss., p. 346, pis. cxxiii. cxxiv. 

Pecopteris dentata, Zeiller, Veget. foss. du terr. houil., p. 86, pi. clxviii. figs. 3, 4. 

Cyatheites dentatus, Geinitz, Vers. d. Steinlf. inSachsen, p. 26, pi. xxv. fig. 11 (in part); pi. xxix. 

figs. 10-12; pi. xxx. figs. 1-3 (4?). 
Dactylotheca dentata, Zeiller, Ann. d. sc. not. Bot., 6 B ser., vol. xvi. p. 184, pi. ix. figs. 12-15; 

Bull. soc. geol. d. France, 3o ser., vol. xii. p. 201. 
Senftenbergia plumosa, Stur, Carbon-Flora, pi. li. fig. 2 (3 1). 

Hem arks. — Two distinct forms of this fern occur in Britain, which have 
usually been regarded as distinct species. In the above synonymy I have 
attempted to separate them. 

This species was first described by Artis in 1825, under the name of 
Filicites plumosus, and what I regard as a variety of Artis's plant was described 
by Brongniart as Pec. dentata in 1828. 

After examining numerous specimens of Dactylotheca (Pec.) plumosa and 
Dactylotheca (Pec.) dentata, I have been led to believe that Pec. dentata can 
only be regarded as a well-marked variety of Pec. plumosa, a view that has 
been indicated by Geinitz. # 

The two forms are, however, so well marked that a varietal name